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Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been studied since ancient times and is used across many fields including astronomy, navigation, architecture, engineering, and digital imaging. Trigonometric functions relate ratios of sides of a right triangle to an angle of the triangle. These functions and their relationships are important tools that are applied in problems involving waves, forces, rotations, and more.

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Trigonometry, Applications of Trigonometry CBSE Class X Project

A powerpoint presentation on the topic applications of trigonometry with an introduction to trigonometry.
By Spandan Bhattacharya
Student

Trigonometry

This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.

Math project some applications of trigonometry

Trigonometry deals with relationships between sides and angles of triangles. It has many applications including calculating heights and distances that are otherwise difficult to measure directly. For example, Thales of Miletus used trigonometry to calculate the height of the Great Pyramid in Egypt by comparing the lengths of shadows at different times of day. Later, Hipparchus constructed trigonometric tables and used trigonometry and angular measurements to determine the distance to the moon. Today, trigonometry is widely used in fields like surveying, navigation, physics, and engineering.

Introduction to trigonometry

This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities when

Introduction to trignometry

INTRODUCTION TO TRIGNOMETRY OF CLASS 10. IT ALSO INCLUDES ALL TOPIC OF TRIGNOMETRY OF CLASS 10 WITH PHOTOS AND DERIVATIOM

Maths project some applications of trignometry- class10 ppt

The document provides an introduction to trigonometry and its applications. It discusses how trigonometry deals with triangles, particularly right triangles, and involves angles and relationships between sides. The document then gives examples of using basic trigonometric ratios like sine, cosine, and tangent to solve problems involving unknown heights or distances. It provides historical context on how trigonometry was used in ancient times for applications like determining the height of structures. Overall, the document outlines fundamental trigonometric concepts and illustrates how trigonometry can be applied to calculate unknown measurements.

Trigonometry presentation

Trigonometry is the study of triangles and their relationships. The document discusses how trigonometry is used in fields like architecture, astronomy, geology, and for measuring distances and heights. It provides examples of how trigonometry can be used to calculate the height of a building given the distance and angle of elevation to its top.

Trigonometry project

Trigonometry is the branch of mathematics dealing with triangles and trigonometric functions of angles. It is derived from Greek words meaning "three angles" and "measure". Trigonometry specifically studies relationships between sides and angles of triangles, and calculations based on trigonometric functions like sine, cosine, and tangent. Trigonometry has many applications in fields like astronomy, navigation, architecture, engineering, and more.

Trigonometry, Applications of Trigonometry CBSE Class X Project

A powerpoint presentation on the topic applications of trigonometry with an introduction to trigonometry.
By Spandan Bhattacharya
Student

Trigonometry

This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.

Math project some applications of trigonometry

Trigonometry deals with relationships between sides and angles of triangles. It has many applications including calculating heights and distances that are otherwise difficult to measure directly. For example, Thales of Miletus used trigonometry to calculate the height of the Great Pyramid in Egypt by comparing the lengths of shadows at different times of day. Later, Hipparchus constructed trigonometric tables and used trigonometry and angular measurements to determine the distance to the moon. Today, trigonometry is widely used in fields like surveying, navigation, physics, and engineering.

Introduction to trigonometry

This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities when

Introduction to trignometry

INTRODUCTION TO TRIGNOMETRY OF CLASS 10. IT ALSO INCLUDES ALL TOPIC OF TRIGNOMETRY OF CLASS 10 WITH PHOTOS AND DERIVATIOM

Maths project some applications of trignometry- class10 ppt

The document provides an introduction to trigonometry and its applications. It discusses how trigonometry deals with triangles, particularly right triangles, and involves angles and relationships between sides. The document then gives examples of using basic trigonometric ratios like sine, cosine, and tangent to solve problems involving unknown heights or distances. It provides historical context on how trigonometry was used in ancient times for applications like determining the height of structures. Overall, the document outlines fundamental trigonometric concepts and illustrates how trigonometry can be applied to calculate unknown measurements.

Trigonometry presentation

Trigonometry is the study of triangles and their relationships. The document discusses how trigonometry is used in fields like architecture, astronomy, geology, and for measuring distances and heights. It provides examples of how trigonometry can be used to calculate the height of a building given the distance and angle of elevation to its top.

Trigonometry project

Trigonometry is the branch of mathematics dealing with triangles and trigonometric functions of angles. It is derived from Greek words meaning "three angles" and "measure". Trigonometry specifically studies relationships between sides and angles of triangles, and calculations based on trigonometric functions like sine, cosine, and tangent. Trigonometry has many applications in fields like astronomy, navigation, architecture, engineering, and more.

trigonometry and application

Trigonometry is derived from Greek words meaning "three angles" and "measure". It deals with relationships between sides and angles of triangles, especially right triangles. The document discusses the history of trigonometry dating back to ancient Egypt and Babylon, and how it advanced through the works of Greek astronomer Hipparchus and Ptolemy. It also discusses the six trigonometric ratios and their formulas, various trigonometric identities, and applications of trigonometry in fields like architecture, engineering, astronomy, music, optics, and more.

Ppt on trignometry by damini

This project on trigonometry was designed by two 10th grade students to introduce various topics in trigonometry. It includes sections on the introduction and definition of trigonometry, trigonometric ratios and their names in a right triangle, examples of applying ratios to find unknown sides, reciprocal identities of ratios, types of problems involving calculating ratios and evaluating expressions, value tables for common angles, formulas relating ratios, and main trigonometric identities. The project was created under the guidance of the students' mathematics teacher.

Maths project --some applications of trignometry--class 10

Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.

Trigonometry

Trigonometry deals with triangles and the angles between sides. The main trigonometric ratios are defined using the sides of a right triangle: sine, cosine, and tangent. Trigonometric functions can convert between degrees and radians. Standard angle positions and trigonometric identities relate trig functions of summed and subtracted angles. The sine and cosine rules relate the sides and angles of any triangle, allowing for calculations of missing sides or angles given other information. Unit circle graphs further illustrate trigonometric functions.

Trigonometry

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has many applications in fields like architecture, astronomy, engineering, and more. The document provides background on trigonometry, defines trigonometric functions and ratios, discusses right triangles, and gives several examples of how trigonometry is used in areas like navigation, construction, and digital imaging.

Trigonometry maths school ppt

Trigonometry is the branch of mathematics that deals with triangles, especially right triangles. It has been used for over 4000 years, originally to calculate sundials. Key trigonometric functions are the sine, cosine, and tangent, which relate the angles and sides of a right triangle. Trigonometric identities and the trig functions of complementary angles are also discussed. Trigonometry has many applications, including in astronomy, navigation, engineering, optics, and more. It allows curved surfaces to be approximated in architecture using flat panels at angles.

Introduction To Trigonometry

This document provides an introduction to trigonometric ratios and identities. It defines the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) for an acute angle in a right triangle. It gives the specific trigonometric ratios for angles of 0°, 45°, 30°, 60°, and 90°. It also establishes the identities relating trigonometric ratios of complementary angles and the Pythagorean identities relating sine, cosine, tangent, cotangent, secant, and cosecant. Examples are provided to demonstrate how to use trigonometric identities to determine ratios when one ratio is known.

Height and distances

Trigonometry is used to calculate unknown heights, distances, and angles using relationships between sides and angles of triangles. It was developed by ancient Greek mathematicians like Thales and Hipparchus to solve problems in astronomy and geography. Some key applications include using trigonometric ratios like tangent and cotangent along with known distances and angles of elevation/depression to determine the height of objects like towers, buildings, and mountains when direct measurement is not possible. The document provides historical context and examples to illustrate how trigonometric concepts have been applied to problems involving finding heights, distances, and other unknown measurements through the use of triangles and their properties.

Application of trigonometry

Trigonometry studies triangles and relationships between sides and angles. This document discusses using trigonometric ratios to calculate heights and distances, such as of trees, towers, water tanks, and distance from a ship to a lighthouse. It provides examples of using trigonometry to calculate the height of a tower given the angle of elevation and distance from its base, and the height of a pole given the angle made by the rope tied to its top and the ground.

Class 10 Ch- introduction to trigonometrey

This document provides an introduction to trigonometry, including its history and key concepts. Trigonometry deals with right triangles and relationships between their sides. Important concepts discussed include the trigonometric ratios (sine, cosine, tangent etc.), Pythagorean theorem, and applications to fields like construction, astronomy, and engineering. An example problem demonstrates using trigonometric functions to calculate the height of a flagpole given the angle of elevation and distance from the base.

Trigonometry Presentation For Class 10 Students

Presentation on Trigonometry. A topic for class 10 Students. Has every topic covered for students wanting to make a presentation on Trigonometry. Hope this will help you...........

Introduction to trigonometry

This document provides an introduction to trigonometry. It defines trigonometry as dealing with relations of sides and angles of triangles. It discusses the history of trigonometry and defines the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent). It provides the ratios for some specific angles and identities relating the ratios. It describes applications of trigonometry in fields like astronomy, navigation, architecture, and more.

Trigonometry abhi

Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
Topics:-
Intro, Information, Formulas, Summary and overview

PPT on Trigonometric Functions. Class 11

Trigonometry deals with relationships between sides and angles of triangles. It originated in ancient Greece and was used to calculate sundials. Key concepts include trigonometric functions like sine, cosine and tangent that relate a triangle's angles to its sides. Trigonometric identities and angle formulae allow for the conversion between functions. It has wide applications in fields like astronomy, engineering and navigation.

Some application of trignometry

Trigonometry deals with right triangles and angles, and is used in fields like sound, light, and perceptions of beauty. The document defines common trigonometric terms like angle of elevation, angle of depression, sine, cosine, and tangent. It provides examples of using trigonometric functions to solve problems like finding the height of a tower or flagpole given angle of elevation measurements. Several practice problems on trigonometry are also presented and solved.

Trigonometry

Trigonometry is the study of relationships between the sides and angles of triangles. It has its origins over 4000 years ago in ancient Egypt, Mesopotamia, and the Indus Valley. The first recorded use was by the Greek mathematician Hipparchus around 150 BC. Trigonometry defines trigonometric functions like sine, cosine, and tangent that relate angles and sides of a triangle. It has many applications in fields like astronomy, navigation, engineering, and more.

Maths ppt on some applications of trignometry

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope and the ground.

Circles IX

Vaibhav Goel presented on circles and their properties. The presentation included definitions of key circle terms like radius, diameter, chord, and arc. It also proved several theorems: equal chords subtend equal angles at the center; a perpendicular from the center bisects a chord; there is one circle through three non-collinear points; equal chords are equidistant from the center; congruent arcs subtend equal angles; and the angle an arc subtends at the center is double that at any other point. The presentation concluded that angles in the same segment are equal and cyclic quadrilaterals have opposite angles summing to 180 degrees.

Mathematics ppt on trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged during the 3rd century BC from applications of geometry to astronomy. Hipparchus is considered the founder of trigonometry, compiling the first trigonometric table in the 2nd century BC. Key trigonometric functions like sine, cosine, and tangent were discovered between the 5th-10th centuries CE by mathematicians including Aryabhata, Muhammad ibn Musa al-Khwarizmi, and Abu al-Wafa. Trigonometry is applied to calculate angles of elevation and depression used in applications like determining the angle an airplane is viewed from the ground.

Applications of trignometry

Trigonometry is a branch of mathematics used to define relationships between sides and angles of triangles, especially right triangles. It has applications in fields like architecture, astronomy, geology, navigation, and oceanography. Trigonometric functions like sine, cosine, and tangent are ratios that relate sides and angles, and trigonometry allows distances, heights, and depths to be easily calculated. Architects use trigonometry to design buildings, astronomers use it to measure distances to stars, and geologists use it to determine slope stability.

history of trigonometry

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.

History of trigonometry clasical - animated

Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometric Functions

trigonometry and application

Trigonometry is derived from Greek words meaning "three angles" and "measure". It deals with relationships between sides and angles of triangles, especially right triangles. The document discusses the history of trigonometry dating back to ancient Egypt and Babylon, and how it advanced through the works of Greek astronomer Hipparchus and Ptolemy. It also discusses the six trigonometric ratios and their formulas, various trigonometric identities, and applications of trigonometry in fields like architecture, engineering, astronomy, music, optics, and more.

Ppt on trignometry by damini

This project on trigonometry was designed by two 10th grade students to introduce various topics in trigonometry. It includes sections on the introduction and definition of trigonometry, trigonometric ratios and their names in a right triangle, examples of applying ratios to find unknown sides, reciprocal identities of ratios, types of problems involving calculating ratios and evaluating expressions, value tables for common angles, formulas relating ratios, and main trigonometric identities. The project was created under the guidance of the students' mathematics teacher.

Maths project --some applications of trignometry--class 10

Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.

Trigonometry

Trigonometry deals with triangles and the angles between sides. The main trigonometric ratios are defined using the sides of a right triangle: sine, cosine, and tangent. Trigonometric functions can convert between degrees and radians. Standard angle positions and trigonometric identities relate trig functions of summed and subtracted angles. The sine and cosine rules relate the sides and angles of any triangle, allowing for calculations of missing sides or angles given other information. Unit circle graphs further illustrate trigonometric functions.

Trigonometry

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has many applications in fields like architecture, astronomy, engineering, and more. The document provides background on trigonometry, defines trigonometric functions and ratios, discusses right triangles, and gives several examples of how trigonometry is used in areas like navigation, construction, and digital imaging.

Trigonometry maths school ppt

Trigonometry is the branch of mathematics that deals with triangles, especially right triangles. It has been used for over 4000 years, originally to calculate sundials. Key trigonometric functions are the sine, cosine, and tangent, which relate the angles and sides of a right triangle. Trigonometric identities and the trig functions of complementary angles are also discussed. Trigonometry has many applications, including in astronomy, navigation, engineering, optics, and more. It allows curved surfaces to be approximated in architecture using flat panels at angles.

Introduction To Trigonometry

This document provides an introduction to trigonometric ratios and identities. It defines the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) for an acute angle in a right triangle. It gives the specific trigonometric ratios for angles of 0°, 45°, 30°, 60°, and 90°. It also establishes the identities relating trigonometric ratios of complementary angles and the Pythagorean identities relating sine, cosine, tangent, cotangent, secant, and cosecant. Examples are provided to demonstrate how to use trigonometric identities to determine ratios when one ratio is known.

Height and distances

Trigonometry is used to calculate unknown heights, distances, and angles using relationships between sides and angles of triangles. It was developed by ancient Greek mathematicians like Thales and Hipparchus to solve problems in astronomy and geography. Some key applications include using trigonometric ratios like tangent and cotangent along with known distances and angles of elevation/depression to determine the height of objects like towers, buildings, and mountains when direct measurement is not possible. The document provides historical context and examples to illustrate how trigonometric concepts have been applied to problems involving finding heights, distances, and other unknown measurements through the use of triangles and their properties.

Application of trigonometry

Trigonometry studies triangles and relationships between sides and angles. This document discusses using trigonometric ratios to calculate heights and distances, such as of trees, towers, water tanks, and distance from a ship to a lighthouse. It provides examples of using trigonometry to calculate the height of a tower given the angle of elevation and distance from its base, and the height of a pole given the angle made by the rope tied to its top and the ground.

Class 10 Ch- introduction to trigonometrey

This document provides an introduction to trigonometry, including its history and key concepts. Trigonometry deals with right triangles and relationships between their sides. Important concepts discussed include the trigonometric ratios (sine, cosine, tangent etc.), Pythagorean theorem, and applications to fields like construction, astronomy, and engineering. An example problem demonstrates using trigonometric functions to calculate the height of a flagpole given the angle of elevation and distance from the base.

Trigonometry Presentation For Class 10 Students

Presentation on Trigonometry. A topic for class 10 Students. Has every topic covered for students wanting to make a presentation on Trigonometry. Hope this will help you...........

Introduction to trigonometry

This document provides an introduction to trigonometry. It defines trigonometry as dealing with relations of sides and angles of triangles. It discusses the history of trigonometry and defines the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent). It provides the ratios for some specific angles and identities relating the ratios. It describes applications of trigonometry in fields like astronomy, navigation, architecture, and more.

Trigonometry abhi

Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
Topics:-
Intro, Information, Formulas, Summary and overview

PPT on Trigonometric Functions. Class 11

Trigonometry deals with relationships between sides and angles of triangles. It originated in ancient Greece and was used to calculate sundials. Key concepts include trigonometric functions like sine, cosine and tangent that relate a triangle's angles to its sides. Trigonometric identities and angle formulae allow for the conversion between functions. It has wide applications in fields like astronomy, engineering and navigation.

Some application of trignometry

Trigonometry deals with right triangles and angles, and is used in fields like sound, light, and perceptions of beauty. The document defines common trigonometric terms like angle of elevation, angle of depression, sine, cosine, and tangent. It provides examples of using trigonometric functions to solve problems like finding the height of a tower or flagpole given angle of elevation measurements. Several practice problems on trigonometry are also presented and solved.

Trigonometry

Trigonometry is the study of relationships between the sides and angles of triangles. It has its origins over 4000 years ago in ancient Egypt, Mesopotamia, and the Indus Valley. The first recorded use was by the Greek mathematician Hipparchus around 150 BC. Trigonometry defines trigonometric functions like sine, cosine, and tangent that relate angles and sides of a triangle. It has many applications in fields like astronomy, navigation, engineering, and more.

Maths ppt on some applications of trignometry

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope and the ground.

Circles IX

Vaibhav Goel presented on circles and their properties. The presentation included definitions of key circle terms like radius, diameter, chord, and arc. It also proved several theorems: equal chords subtend equal angles at the center; a perpendicular from the center bisects a chord; there is one circle through three non-collinear points; equal chords are equidistant from the center; congruent arcs subtend equal angles; and the angle an arc subtends at the center is double that at any other point. The presentation concluded that angles in the same segment are equal and cyclic quadrilaterals have opposite angles summing to 180 degrees.

Mathematics ppt on trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged during the 3rd century BC from applications of geometry to astronomy. Hipparchus is considered the founder of trigonometry, compiling the first trigonometric table in the 2nd century BC. Key trigonometric functions like sine, cosine, and tangent were discovered between the 5th-10th centuries CE by mathematicians including Aryabhata, Muhammad ibn Musa al-Khwarizmi, and Abu al-Wafa. Trigonometry is applied to calculate angles of elevation and depression used in applications like determining the angle an airplane is viewed from the ground.

Applications of trignometry

Trigonometry is a branch of mathematics used to define relationships between sides and angles of triangles, especially right triangles. It has applications in fields like architecture, astronomy, geology, navigation, and oceanography. Trigonometric functions like sine, cosine, and tangent are ratios that relate sides and angles, and trigonometry allows distances, heights, and depths to be easily calculated. Architects use trigonometry to design buildings, astronomers use it to measure distances to stars, and geologists use it to determine slope stability.

trigonometry and application

trigonometry and application

Ppt on trignometry by damini

Ppt on trignometry by damini

Maths project --some applications of trignometry--class 10

Maths project --some applications of trignometry--class 10

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry maths school ppt

Trigonometry maths school ppt

Introduction To Trigonometry

Introduction To Trigonometry

Height and distances

Height and distances

Application of trigonometry

Application of trigonometry

Class 10 Ch- introduction to trigonometrey

Class 10 Ch- introduction to trigonometrey

Trigonometry Presentation For Class 10 Students

Trigonometry Presentation For Class 10 Students

Introduction to trigonometry

Introduction to trigonometry

Trigonometry abhi

Trigonometry abhi

PPT on Trigonometric Functions. Class 11

PPT on Trigonometric Functions. Class 11

Some application of trignometry

Some application of trignometry

Trigonometry

Trigonometry

Maths ppt on some applications of trignometry

Maths ppt on some applications of trignometry

Circles IX

Circles IX

Mathematics ppt on trigonometry

Mathematics ppt on trigonometry

Applications of trignometry

Applications of trignometry

history of trigonometry

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.

History of trigonometry clasical - animated

Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometric Functions

Trigonometric Ratios

The document discusses trigonometric ratios and right triangles. It defines trigonometric ratios like sine, cosine, and tangent using the sides of a right triangle. It also describes two special right triangles - the 30-60-90 triangle and the 45-45-90 triangle - that are used often in trigonometry.

Trigonometry Lesson: Introduction & Basics

This trigonometry lesson introduces important trigonometry topics including the Pythagorean theorem, special right triangles, trigonometric functions, the law of cosines and sines, identities, and half and double angle formulas. Key concepts are the measurement of triangles, trigonometric ratios related to sides of right triangles, and trigonometric functions defined in relation to angles. Examples are provided to demonstrate applying the Pythagorean theorem and laws of cosines and sines to solve for unknown sides of triangles.

Real World Application of Trigonometry

Trigonometry is a branch of mathematics that studies triangles and their relationships. The document discusses how trigonometry is used in the fields of architecture, astronomy, and geology. In architecture, trigonometry is used to calculate angles to ensure structural stability and safety. Astronomers use trigonometry and concepts like parallax to calculate distances between stars. Geologists use trigonometry to estimate true dip angles of bedding to determine slope stability important for building foundations.

Junior school math quiz final

The document outlines the format and questions for a math quiz with two levels and several rounds. It will include identifying shapes and patterns, solving math problems, and trick questions. Level 1 has two rounds focused on numbers, with 6 questions in each round worth 1 minute each. Level 2 has two visual rounds with 5 questions worth either 1 or 2 minutes each. The rounds continue with more challenging math problems using numbers, shapes, puzzles, and rapid fire questions.

Middle school math quiz

This document provides details of a mathematics quiz for level II students, including the format, topics, and sample questions. The quiz has three main sections - a visual round with 6 questions in 6 minutes, a rapid fire round with 6 questions in 12 minutes, and a math models round where students are given materials to model math concepts and are asked 6 questions in 10 minutes randomly selected. Sample questions cover topics like geometry, algebra, fractions, time, logic puzzles, and more. The document aims to give an overview of the structure and difficulty of the quiz.

Natural disaster

Natural disasters are major changes that can damage the earth's land and threaten human and animal lives. They include earthquakes caused by shifting tectonic plates that release shock waves, prolonged droughts like the one in Africa in 1968 that lasted 5 years, powerful cyclones with swirling winds that can destroy infrastructure, flooding from heavy rain or snowmelt that causes rivers to overflow their banks, and wildfires ignited by lightning or humans that can spread quickly with wind.

Personal branding Advisory-AnaMariaGavrila_2016

This document provides information about personal branding advisory services offered by Ana-Maria Gavrilă. She has 14 years of experience in public relations working for big consulting firms. Her services include personal branding audits, communication strategies, branding positioning, media relations, training in branding fundamentals, communication skills, and networking. She contributes articles to top business publications in Romania and provides personal branding advisory and training to corporate and entrepreneur communities.

We Can't Delay!

The document discusses how technology integration in the classroom is important because the world is changing faster than ever before. It argues that instructional technology methods should be tailored to match specific teaching and learning practices, and that both new and old strategies have value. To effectively integrate technology, teachers need a combination of technological, pedagogical, and content knowledge, and they should start implementing technology in the classroom now.

TEDxTorVergataU - Presentation

Presentation dedicated to univerisy's staff

Constituição

1) A Constituição da República de Moçambique estabelece os princípios fundamentais do Estado, incluindo que Moçambique é uma república independente, soberana, democrática e de justiça social.
2) O documento define a nacionalidade moçambicana, o território, a organização territorial do país, e objetivos como a defesa da independência, unidade nacional e promoção dos direitos humanos.
3) A política externa de Moçambique baseia-se em princípios como respeito mútuo e não

history of trigonometry

history of trigonometry

History of trigonometry clasical - animated

History of trigonometry clasical - animated

Trigonometric Ratios

Trigonometric Ratios

Trigonometry Lesson: Introduction & Basics

Trigonometry Lesson: Introduction & Basics

Real World Application of Trigonometry

Real World Application of Trigonometry

Junior school math quiz final

Junior school math quiz final

Middle school math quiz

Middle school math quiz

Natural disaster

Natural disaster

Personal branding Advisory-AnaMariaGavrila_2016

Personal branding Advisory-AnaMariaGavrila_2016

สถานการณ์ปัญหาบทที่ 3

สถานการณ์ปัญหาบทที่ 3

We Can't Delay!

We Can't Delay!

สถานการณ์ปัญหาบทที่ 7

สถานการณ์ปัญหาบทที่ 7

LOS CINCO SENTIDOS

LOS CINCO SENTIDOS

TEDxTorVergataU - Presentation

TEDxTorVergataU - Presentation

Constituição

Constituição

Trigonometry maths x vikas kumar

Vikas Kumar presented on trigonometry. Trigonometry deals with relationships between sides and angles of triangles, specifically right triangles. It has its origins in ancient Egypt, Mesopotamia and India over 4000 years ago. Trigonometric functions like sine, cosine and tangent are used to relate angles to sides in right triangles. Trigonometry has many applications including astronomy, architecture, digital imaging, waves and more due to its ability to model periodic phenomena and approximate curves and surfaces with triangles.

Trigonometry maths x vikas kumar

Vikas Kumar presented on trigonometry, beginning with definitions and history. Trigonometry deals with relationships in triangles, especially right triangles, and trigonometric functions like sine, cosine, and tangent. It has many applications including architecture, astronomy, digital imaging, waves, and engineering. Trigonometry underlies techniques like triangulation used in fields as diverse as mapmaking, medical imaging, and computer graphics.

Trigonometry maths x vikas kumar

Vikas Kumar presented on trigonometry, beginning with definitions and history. Trigonometry deals with relationships in triangles, especially right triangles, and trigonometric functions like sine, cosine, and tangent. It has many applications including architecture, astronomy, digital imaging, waves, and engineering. Trigonometry underlies techniques like triangulation used in fields as diverse as mapmaking, medical imaging, and computer graphics.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been used for over 4000 years, originally to calculate sundials and now in fields like navigation, engineering, and astronomy. Trigonometry specifically studies right triangles, where one angle is 90 degrees. The Pythagorean theorem relates the sides of a right triangle, and trigonometric ratios like sine, cosine, and tangent are used to calculate unknown sides and angles based on known values. Trigonometry has many applications in areas involving waves, geometry, and modeling real-world phenomena.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been used for over 4000 years, originally to calculate sundials and now in fields like astronomy, engineering, and digital imaging. Trigonometry specifically studies right triangles and defines trigonometric functions like sine, cosine, and tangent that relate a triangle's angles and sides. Key concepts include trigonometric ratios, the Pythagorean theorem, trigonometric identities, and applications to problems involving distance, direction, and waves.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been developed and used for over 4000 years, originating in ancient civilizations for purposes like calculating sundials. A key foundation is the right triangle, where one angle is 90 degrees. Pythagoras' theorem relates the sides of a right triangle, and trigonometric ratios like sine, cosine, and tangent define relationships between sides and angles. Trigonometry has many applications, from astronomy and navigation to engineering, physics, and digital imaging.

Trigonometry

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been studied since ancient civilizations over 4000 years ago and is used in many fields today including architecture, astronomy, engineering, and more. Trigonometric functions relate ratios of sides in a right triangle to the angles of the triangle. These functions and their relationships are important tools that allow calculations and problem solving across various domains.

Trigonometry

Trigonometry is the study of measuring triangles and angles. It originated over 4000 years ago in ancient Egypt, Mesopotamia, and India to calculate sundials and solve triangles. Key developments include Hipparchus' trig tables in 150 BC and the Sulba Sutras in 800-500 BC. Trigonometry has many applications including astronomy, navigation, music, acoustics, optics, engineering, and more due to its ability to model waves and approximate curved surfaces with triangles. It remains an important area of ongoing research.

Trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged from applications of geometry to astronomy in the 3rd century BC. Trigonometric functions relate ratios of sides of right triangles to angles and allow for determination of all angles and sides from just one angle and one side. Trigonometry is used in many fields including astronomy, navigation, music, acoustics, optics, engineering, and more due to applications of triangulation and modeling periodic functions.

Introduction of trigonometry

Lesson plan on introduction of trigonometry, students must aware about the history , concepts to be done, what common error they commit and what are the scope of this topic in careers

Trigonometry class10.pptx

This document provides an overview of trigonometry. It defines trigonometry as dealing with relationships between sides and angles of triangles, particularly right triangles. The origins of trigonometry can be traced back 4000 years to ancient civilizations. Key concepts discussed include right triangles, the Pythagorean theorem, trigonometric ratios like sine, cosine and tangent, and applications of trigonometry in fields like construction, astronomy, and engineering. Examples are provided for using trigonometric functions to solve problems involving heights and distances.

นำเสนอตรีโกณมิติจริง

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been used for thousands of years in fields like astronomy, navigation, architecture, engineering, and more modern fields like digital imaging and computer graphics. Trigonometric functions define ratios between sides of a right triangle and are used to solve for unknown sides and angles. Common applications include calculating distances, heights, satellite positioning, and modeling waves and vibrations.

Trigonometry

Trigonometry is the branch of mathematics that deals with triangles and their angles. It originated over 4000 years ago in ancient Egypt, Mesopotamia, and India, where it was used to calculate sundials and circle squares. Key contributors include Hipparchus, who compiled trigonometric tables using sines, and ancient Indian mathematicians who computed sine values. Trigonometry defines functions like sine, cosine, and tangent that relate a triangle's angles and sides. It has many applications, including astronomy, navigation, engineering, acoustics, and more.

presentation_trigonometry-161010073248_1596171933_389536.pdf

Trigonometry deals with relationships between the sides and angles of triangles. It originated over 4000 years ago in ancient civilizations for purposes like calculating sundials. Key concepts include defining right triangles, the Pythagorean theorem relating sides, and trigonometric ratios relating sides to angles. Trigonometry has many applications including construction, astronomy, navigation, and other fields using triangle relationships.

Trigonometry

Trigonometry is the branch of mathematics that deals with relationships between sides and angles of triangles, especially right triangles. It has its origins in ancient civilizations over 4000 years ago and was originally used to calculate sundials. Key concepts in trigonometry include the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) that relate ratios of sides and angles in triangles. Trigonometric functions have many applications in fields like astronomy, navigation, engineering, and more.

Trigonometry

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles in triangles. The key concepts are the trigonometric functions sine, cosine, and tangent, which describe ratios of sides of a right triangle. Trigonometry has applications in fields like navigation, music, engineering, and more. It has evolved significantly from its origins in ancient Greece and India, with modern definitions extending it to all real and complex number arguments.

trigonometry and applications

This document provides an overview of trigonometry and its applications. It begins with definitions of trigonometry, its history and etymology. It discusses trigonometric functions like sine, cosine and their properties. It covers trigonometric identities and applications in fields like astronomy, navigation, acoustics and more. It also discusses angle measurement in degrees and radians. Laws of sines and cosines are explained. The document concludes with examples of trigonometric equations and their applications.

trigonometryabhi-161010073248.pptx

Trigonometry deals with relationships between the sides and angles of triangles, specifically right triangles where one angle is 90 degrees. It originated over 4000 years ago with ancient Egyptian, Mesopotamian, and Indus Valley civilizations, possibly for calculating sundials. Key concepts in trigonometry include the trigonometric functions sine, cosine, and tangent, which relate a triangle's angles to its sides, as well as Pythagoras' theorem for relating sides in a right triangle. Trigonometry has many applications in fields like construction, astronomy, navigation, acoustics, and engineering.

Application of Trigonometry in Data Science and AI

In this ppt we basically gives application of Trigonometry in data science and Artificial intelligence

Trigo

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged from applications of geometry to astronomy in the 3rd century BC. Trigonometric functions relate ratios of sides of a right triangle to its angles, and are now used across many fields including physics, engineering, music, astronomy, and more. Key concepts include defining the sine, cosine, and tangent functions; extending them to angles beyond 90 degrees using the unit circle; and common trigonometric identities and formulas used for solving triangles.

Trigonometry maths x vikas kumar

Trigonometry maths x vikas kumar

Trigonometry maths x vikas kumar

Trigonometry maths x vikas kumar

Trigonometry maths x vikas kumar

Trigonometry maths x vikas kumar

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Introduction of trigonometry

Introduction of trigonometry

Trigonometry class10.pptx

Trigonometry class10.pptx

นำเสนอตรีโกณมิติจริง

นำเสนอตรีโกณมิติจริง

Trigonometry

Trigonometry

presentation_trigonometry-161010073248_1596171933_389536.pdf

presentation_trigonometry-161010073248_1596171933_389536.pdf

Trigonometry

Trigonometry

Trigonometry

Trigonometry

trigonometry and applications

trigonometry and applications

trigonometryabhi-161010073248.pptx

trigonometryabhi-161010073248.pptx

Application of Trigonometry in Data Science and AI

Application of Trigonometry in Data Science and AI

Trigo

Trigo

Energy efficiency

Energy efficiency refers to reducing the amount of energy required to provide products and services. For example, insulating a home allows it to use less energy for heating and cooling while maintaining a comfortable temperature. Using fluorescent or LED bulbs instead of incandescent bulbs reduces the energy needed for the same level of illumination. Modern appliances like refrigerators and washing machines also use significantly less energy than older models. Individual actions such as switching off unused lights and appliances, closing doors and windows while using AC, and choosing more efficient products can all help conserve electricity.

Geometry the congruence of triangles

The document discusses congruent triangles and different postulates that can be used to prove triangles are congruent. It states that triangles can be proved congruent without showing all three pairs of congruent sides and angles. It then provides examples of different postulates like AAS, SAS, and SSS that can be used to prove triangles congruent. It also discusses isosceles triangles and how if two isosceles triangles share a common base, the line segment joining their vertices will bisect the common base at a right angle.

World war I

World War I began on July 28, 1914 and ended on November 11, 1918. It resulted in almost 8 million deaths, with Russia experiencing the most at 1.7 million. Militarism, imperialism, nationalism, and alliances between European powers all contributed to the outbreak of the war. The war was the first to utilize advanced weapons and tactics on a massive scale across trenches along the Western Front. It ultimately redrew the map of Europe following hostilities.

Solar energy

The document discusses the use of solar energy for water heating. It begins by defining solar energy and describing the two main forms: passive and active solar energy. It then discusses using solar energy to heat water for homes through solar water heating systems. These systems use solar panels to collect heat from the sun and transfer it to heat water stored in a hot water cylinder. The water can then be further heated using a boiler if additional heating is needed. The document provides details on different types of solar water heating systems and their components. In conclusion, it states that solar water heating is a renewable and cost-effective way to generate hot water for homes.

The human body systems2

The document summarizes the major human body systems and how they work. It discusses the digestive system, skeletal system, circulatory system, muscular system, nervous system, and respiratory system. For each system it describes the main organs and their functions in transporting, protecting, and supporting the tissues and cells of the body.

Triangles ix

This document provides information about congruence of triangles from a geometry textbook. It includes definitions of congruent figures and associating real numbers with lengths and angles. It describes the one-to-one correspondence test for congruence of triangles. It discusses sufficient conditions for congruence including SAS, SSS, ASA, and SAA. It presents activities and examples verifying these tests and exploring properties of isosceles and equilateral triangles. The document encourages critical thinking through "Think it Over" prompts and upgrading the chapter with additional content.

Rotation and revolution

The Earth rotates on its axis from West to East, causing day and night. It also revolves around the Sun, causing seasons. The Equator divides the Earth into the Northern and Southern Hemispheres. Rotation and revolution are responsible for different weather patterns and climates in different places over time. Sea breezes occur during the day as warmer air rises over heated land, drawing in cooler air from the sea.

Ppt on living things

1. Producers, consumers, scavengers, and decomposers are the four main categories of living things. Producers like plants can make their own food through photosynthesis, while consumers depend on other organisms for food.
2. Scavengers feed on dead animals, acting as environment cleaners. Decomposers like fungi and bacteria break down dead organisms, recycling nutrients in the soil.
3. Plants, animals, and decomposers are interdependent. Pollinators like bees help plants reproduce, and animals disperse seeds. Decomposers break down waste and make nutrients available to plants.

Holy river ganga

The Ganges River originates in the Himalayas and flows south through India and into Bangladesh before emptying into the Bay of Bengal. It is over 2,500 km long, making it the longest river in India and second longest in the world. The Ganges basin supports a large population and highly productive agriculture. Over 400 million people depend on the Ganges for drinking water, bathing, irrigation, industry, and other needs. However, the river is also severely polluted from sewage and industrial waste from the many cities and towns along its banks.

Quadrilaterals

1) A quadrilateral is a plane figure with four sides and four vertices. There are different types of quadrilaterals classified based on their properties.
2) Parallelograms have two sets of parallel sides and opposite angles are equal. Specific types of parallelograms include rectangles, rhombi, and squares.
3) Trapezoids have only one set of parallel sides, while kites have two pairs of equal adjacent sides that meet at equal angles.

Maths puzzle

The document contains 10 puzzles involving patterns, numbers, shapes, and logic. Each puzzle poses a question or challenge such as finding the odd one out, completing patterns, identifying differences, solving magic squares, and determining multiplications. The puzzles increase in complexity, covering topics like triangle patterns, mixed rules, star shapes, and drawing shapes to complete 3x3 grids.

Polynomials

Polynomials are mathematical expressions constructed from variables and constants using addition, subtraction, multiplication, and exponents of whole numbers. They appear in many areas of mathematics and science. Polynomials can be used to form equations that model problems in various domains. They also define polynomial functions that are used in fields like physics, chemistry, economics, and social sciences. Polynomials are classified based on their degree, with linear polynomials having degree 1 and quadratic polynomials degree 2. The maximum number of zeroes a polynomial can have is equal to its degree.

Making of the indian constitution by madhavi mahajan

The document summarizes the process of drafting and adopting the Constitution of India. It describes how the Constituent Assembly was formed through elections in British India in 1946. Key people involved in drafting the Constitution are mentioned, such as B.R. Ambedkar who chaired the Drafting Committee. The document also provides details on the structure of the Constitution, including the inclusion of Fundamental Rights, Directive Principles, and the Preamble. It notes the Constitution was formally adopted on November 26, 1949 by the Constituent Assembly.

Maps and location

Maps provide important information about locations and landmarks to help with navigation. They use a standardized set of symbols, colors, scales, and directions that are universally understood. Key features include water depicted in blue, elevations shown in brown/yellow, and a map key to explain symbols. Maps are an important way to represent and share geographic information about places.

Ill effects of alcohol

Alcohol consumption can have several ill effects:
1. It slows down brain activity and nervous system function, impairing judgment and reaction time. This increases the risk of road accidents from drunken driving.
2. It lowers inhibitions, making drunk people more quarrelsome. This leads to increased violence and crime.
3. Heavy drinking on a single occasion can cause staggered movement, slurred speech, blurred vision, dizziness, and vomiting. Drinking large quantities can make a person pass out.

Human system

Our body contains many internal organs that work together in organ systems to carry out vital functions. There are two main types of organs - external organs that can be seen, and internal organs that cannot be seen and are protected by bones. The internal organs are grouped into organ systems like the circulatory, respiratory, and digestive systems to perform functions such as transporting blood, supplying oxygen, and breaking down food.

Electrical safetyathome

This document provides information about home electricity usage and safety. It summarizes that refrigeration accounts for 31% of home electricity use, while heating accounts for 12% and cooling accounts for 11%. It also explains the basic components of a home's electrical system, including the electric meter, service panel, circuits, and grounding. The document discusses older wiring systems like knob-and-tube and aluminum wiring that can pose fire hazards, and emphasizes having a grounded electrical system and updating to tamper-resistant and GFCI outlets for safety. It concludes by offering free safety demonstrations from San Miguel Power to local groups.

Components of food class iv

The document discusses the main components of food: carbohydrates, fibers, minerals, proteins, and vitamins. Carbohydrates provide the body's main source of energy and are broken down into glucose. Fiber is found in plant foods and has health benefits. Minerals are essential nutrients needed for processes like heart function and bone formation. Proteins are needed to build muscles and tissues. Vitamins are required for regulating bodily functions and must be obtained through diet.

Congruent triangles theorem

This document discusses triangle congruence theorems. It defines the five main congruence theorems: ASA, SAS, SSS, AAS, and introduces four additional theorems for right triangles only: HL, HA, LL, LA. Examples are provided to demonstrate applying each theorem to determine if two triangles are congruent based on given side or angle information.

Natural disaster (hindi}

Natural disaster (hindi}

Energy efficiency

Energy efficiency

Geometry the congruence of triangles

Geometry the congruence of triangles

World war I

World war I

Solar energy

Solar energy

The human body systems2

The human body systems2

Triangles ix

Triangles ix

Rotation and revolution

Rotation and revolution

Ppt on living things

Ppt on living things

Holy river ganga

Holy river ganga

Quadrilaterals

Quadrilaterals

Maths puzzle

Maths puzzle

Polynomials

Polynomials

Making of the indian constitution by madhavi mahajan

Making of the indian constitution by madhavi mahajan

Maps and location

Maps and location

Ill effects of alcohol

Ill effects of alcohol

Human system

Human system

Electrical safetyathome

Electrical safetyathome

Components of food class iv

Components of food class iv

Congruent triangles theorem

Congruent triangles theorem

How to Fix the Import Error in the Odoo 17

An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.

Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx

Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024

ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf

it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.

PIMS Job Advertisement 2024.pdf Islamabad

advasitment of Punjab

Wound healing PPT

This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.

Main Java[All of the Base Concepts}.docx

This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.

Cognitive Development Adolescence Psychology

Cognitive Development Adolescence Psychology

Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...

Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.

BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...

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https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneবাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf

বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...National Information Standards Organization (NISO)

This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.Chapter 4 - Islamic Financial Institutions in Malaysia.pptx

Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia

This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Hindi varnamala | hindi alphabet PPT.pdf

हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com

คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1

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The Diamonds of 2023-2024 in the IGRA collection

A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.

South African Journal of Science: Writing with integrity workshop (2024)

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A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.Pengantar Penggunaan Flutter - Dart programming language1.pptx

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Walmart Business+ and Spark Good for Nonprofits.pdf

"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"

Chapter wise All Notes of First year Basic Civil Engineering.pptx

Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1

How to Fix the Import Error in the Odoo 17

How to Fix the Import Error in the Odoo 17

Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx

Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx

ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf

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PIMS Job Advertisement 2024.pdf Islamabad

PIMS Job Advertisement 2024.pdf Islamabad

Wound healing PPT

Wound healing PPT

Main Java[All of the Base Concepts}.docx

Main Java[All of the Base Concepts}.docx

Cognitive Development Adolescence Psychology

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- 2. 2 Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure). Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees Triangles on a sphere are also studied, in spherical trigonometry. Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, on the trigonometric functions, and with calculations based on these functions. Trigonometry
- 3. 3 History • The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago. • Some experts believe that trigonometry was originally invented to calculate sundials, a traditional exercise in the oldest books • The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. • The Sulba Sutras written in India, between 800 BC and 500 BC, correctly compute the sine of π/4 (45°) as 1/√2 in a procedure for circling the square (the opposite of squaring the circle). • Many ancient mathematicians like Aryabhata, Brahmagupta,Ibn Yunus and Al-Kashi made significant contributions in this field(trigonometry).
- 4. 4 Right Triangle A triangle in which one angle is equal to 90 is called right triangle. The side opposite to the right angle is known as hypotenuse. AB is the hypotenuse The other two sides are known as legs. AC and BC are the legs Trigonometry deals with Right Triangles
- 5. 5 Pythagoras Theorem In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of areas of the squares whose sides are the two legs. In the figure AB2 = BC2 + AC2
- 6. 6 Trigonometric ratios Sine(sin) opposite side/hypotenuse Cosine(cos) adjacent side/hypotenuse Tangent(tan) opposite side/adjacent side Cosecant(cosec) hypotenuse/opposite side Secant(sec) hypotenuse/adjacent side Cotangent(cot) adjacent side/opposite side
- 7. 7 Values of trigonometric function of Angle A sin = a/c cos = b/c tan = a/b cosec = c/a sec = c/b cot = b/a
- 8. 8 Values of Trigonometric function 0 30 45 60 90 Sine 0 0.5 1/ 2 3/2 1 Cosine 1 3/2 1/ 2 0.5 0 Tangent 0 1/ 3 1 3 Not defined Cosecant Not defined 2 2 2/ 3 1 Secant 1 2/ 3 2 2 Not defined Cotangent Not defined 3 1 1/ 3 0
- 9. 9 Calculator This Calculates the values of trigonometric functions of different angles. First Enter whether you want to enter the angle in radians or in degrees. Radian gives a bit more accurate value than Degree. Then Enter the required trigonometric function in the format given below: Enter 1 for sin. Enter 2 for cosine. Enter 3 for tangent. Enter 4 for cosecant. Enter 5 for secant. Enter 6 for cotangent. Then enter the magnitude of angle.
- 10. 10 Trigonometric identities • sin2A + cos2A = 1 • 1 + tan2A = sec2A • 1 + cot2A = cosec2A • sin(A+B) = sinAcosB + cosAsin B • cos(A+B) = cosAcosB – sinAsinB • tan(A+B) = (tanA+tanB)/(1 – tanAtan B) • sin(A-B) = sinAcosB – cosAsinB • cos(A-B)=cosAcosB+sinAsinB • tan(A-B)=(tanA-tanB)(1+tanAtanB) • sin2A =2sinAcosA • cos2A=cos2A - sin2A • tan2A=2tanA/(1-tan2A) • sin(A/2) = {(1-cosA)/2} • Cos(A/2)= {(1+cosA)/2} • Tan(A/2)= {(1-cosA)/(1+cosA)}
- 11. 11 Relation between different Trigonometric Identities • Sine • Cosine • Tangent • Cosecant • Secant • Cotangent
- 12. 12 Angles of Elevation and Depression Line of sight: The line from our eyes to the object, we are viewing. Angle of Elevation:The angle through which our eyes move upwards to see an object above us. Angle of depression:The angle through which our eyes move downwards to see an object below us.
- 13. 13 Problem solved using trigonometric ratios CLICK HERE!
- 14. 14 Applications of Trigonometry • This field of mathematics can be applied in astronomy,navigation, music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.
- 15. 15 Derivations • Most Derivations heavily rely on Trigonometry. Click the hyperlinks to view the derivation • A few such derivations are given below:- • Parallelogram law of addition of vectors. • Centripetal Acceleration. • Lens Formula • Variation of Acceleration due to gravity due to rotation of earth. • Finding angle between resultant and the vector.
- 16. 16 Applications of Trigonometry in Astronomy • Since ancient times trigonometry was used in astronomy. • The technique of triangulation is used to measure the distance to nearby stars. • In 240 B.C., a mathematician named Eratosthenes discovered the radius of the Earth using trigonometry and geometry. • In 2001, a group of European astronomers did an experiment that started in 1997 about the distance of Venus from the Sun. Venus was about 105,000,000 kilometers away from the Sun .
- 17. 17 Application of Trigonometry in Architecture • Many modern buildings have beautifully curved surfaces. • Making these curves out of steel, stone, concrete or glass is extremely difficult, if not impossible. • One way around to address this problem is to piece the surface together out of many flat panels, each sitting at an angle to the one next to it, so that all together they create what looks like a curved surface. • The more regular these shapes, the easier the building process. • Regular flat shapes like squares, pentagons and hexagons, can be made out of triangles, and so trigonometry plays an important role in architecture.
- 18. 18 Waves • The graphs of the functions sin(x) and cos(x) look like waves. Sound travels in waves, although these are not necessarily as regular as those of the sine and cosine functions. • However, a few hundred years ago, mathematicians realized that any wave at all is made up of sine and cosine waves. This fact lies at the heart of computer music. • Since a computer cannot listen to music as we do, the only way to get music into a computer is to represent it mathematically by its constituent sound waves. • This is why sound engineers, those who research and develop the newest advances in computer music technology, and sometimes even composers have to understand the basic laws of trigonometry. • Waves move across the oceans, earthquakes produce shock waves and light can be thought of as traveling in waves. This is why trigonometry is also used in oceanography, seismology, optics and many other fields like meteorology and the physical sciences.
- 19. 19 Digital Imaging • In theory, the computer needs an infinite amount of information to do this: it needs to know the precise location and colour of each of the infinitely many points on the image to be produced. In practice, this is of course impossible, a computer can only store a finite amount of information. • To make the image as detailed and accurate as possible, computer graphic designers resort to a technique called triangulation. • As in the architecture example given, they approximate the image by a large number of triangles, so the computer only needs to store a finite amount of data. • The edges of these triangles form what looks like a wire frame of the object in the image. Using this wire frame, it is also possible to make the object move realistically. • Digital imaging is also used extensively in medicine, for example in CAT and MRI scans. Again, triangulation is used to build accurate images from a finite amount of information. • It is also used to build "maps" of things like tumors, which help decide how x-rays should be fired at it in order to destroy it.
- 20. 20 Conclusion Trigonometry is a branch of Mathematics with several important and useful applications. Hence it attracts more and more research with several theories published year after year Thank You
- 21. 21