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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.

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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

Introduction to trignometry

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

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.

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

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.

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 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.

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

Introduction to trignometry

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

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.

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

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.

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 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 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.

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.

Trigonometry slide presentation

This document provides an overview of trigonometry, including its origins in Greek mathematics, the six main trigonometric functions defined in terms of right triangles, and trigonometric identities. Trigonometry is the study of triangles and relationships between sides and angles, with the six functions—sine, cosine, tangent, cotangent, secant, and cosecant—defined based on ratios of sides. Special angle values and identities are also discussed as important concepts in trigonometry.

Trigonometry

This is a school standard presentation for class 10 students .
It will be very helpful to you all.
Hope you all like this .
And pass your exams with flying colors

Basic trigonometry

This document provides an overview of basic trigonometry. It defines trigonometry as the study of relationships involving lengths and angles of triangles, and notes that it emerged from applications of geometry to astronomy. The document explains the key parts of a right triangle, the trigonometric ratios of sine, cosine and tangent, and the SOHCAHTOA mnemonic. It also covers important angles, Pythagoras' theorem, other trigonometric ratios, the unit circle, and trigonometric functions and identities. Links are provided for additional online resources on trigonometry.

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 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.

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.

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.

Geometry presentation

Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.

Trignometry in daily life

Trigonometry is the branch of mathematics dealing with relationships between sides and angles of triangles. The document traces the origins of common trigonometric functions like sine, cosine, and tangent from ancient Indian and Greek mathematicians. It then explains how trigonometric ratios are used to calculate the angle of elevation of a room by measuring the wall length and diagonal distance and applying the sine ratio formula.

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.

Trigonometry

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.

Pythagoras And The Pythagorean Theorem

Pythagoras was a Greek mathematician born around 570 BCE in Samos, Greece. He founded a school in Croton, Italy where he studied mathematics and developed the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras made many contributions to mathematics and music. He discovered that the musical scale is based on string length ratios and ratios of whole numbers.

Triangles and its properties

The document defines and describes different types of triangles based on their sides and angles. It discusses scalene, isosceles, equilateral, acute-angled, right-angled, and obtuse-angled triangles. It also outlines some key properties of triangles, including that they have three sides and three angles, medians connect vertices to midpoints of opposite sides, altitudes are perpendicular from vertices to opposite sides, exterior angles equal the sum of interior opposite angles, and isosceles triangles have equal angles opposite equal sides. The Pythagorean theorem is also summarized.

Introduction To Trigonometry

It is a ppt on Trigonometry for th students of class 10 .
The basic concepts of trigonometry are provided here with examples Hope that that you like it .!! Thankyou ..!! :)

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.

Class IX Heron's Formula

The document discusses Heron's formula for calculating the area of a triangle. Heron's formula uses the lengths of the three sides of a triangle to calculate its area, rather than requiring the base and height. The formula is defined as the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter (half the perimeter) and a, b, c are the three side lengths. The formula is useful when it is difficult to measure the base and height of a triangle directly. An example problem demonstrates calculating the area of a triangle with side lengths 3cm, 4cm, and 5cm using Heron's formula.

Math lecture 8 (Introduction to Trigonometry)

Trigonometry involves calculating relationships between sides and angles of triangles. The main trigonometric functions are sine, cosine, and tangent, which relate the opposite, adjacent, and hypotenuse sides to an angle. These functions repeat in a repeating pattern as angles increase or decrease by full rotations. Trigonometry is used to solve for unknown sides and angles of triangles.

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 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 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.

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.

Trigonometry slide presentation

This document provides an overview of trigonometry, including its origins in Greek mathematics, the six main trigonometric functions defined in terms of right triangles, and trigonometric identities. Trigonometry is the study of triangles and relationships between sides and angles, with the six functions—sine, cosine, tangent, cotangent, secant, and cosecant—defined based on ratios of sides. Special angle values and identities are also discussed as important concepts in trigonometry.

Trigonometry

This is a school standard presentation for class 10 students .
It will be very helpful to you all.
Hope you all like this .
And pass your exams with flying colors

Basic trigonometry

This document provides an overview of basic trigonometry. It defines trigonometry as the study of relationships involving lengths and angles of triangles, and notes that it emerged from applications of geometry to astronomy. The document explains the key parts of a right triangle, the trigonometric ratios of sine, cosine and tangent, and the SOHCAHTOA mnemonic. It also covers important angles, Pythagoras' theorem, other trigonometric ratios, the unit circle, and trigonometric functions and identities. Links are provided for additional online resources on trigonometry.

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 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.

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.

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.

Geometry presentation

Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.

Trignometry in daily life

Trigonometry is the branch of mathematics dealing with relationships between sides and angles of triangles. The document traces the origins of common trigonometric functions like sine, cosine, and tangent from ancient Indian and Greek mathematicians. It then explains how trigonometric ratios are used to calculate the angle of elevation of a room by measuring the wall length and diagonal distance and applying the sine ratio formula.

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.

Trigonometry

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.

Pythagoras And The Pythagorean Theorem

Pythagoras was a Greek mathematician born around 570 BCE in Samos, Greece. He founded a school in Croton, Italy where he studied mathematics and developed the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras made many contributions to mathematics and music. He discovered that the musical scale is based on string length ratios and ratios of whole numbers.

Triangles and its properties

The document defines and describes different types of triangles based on their sides and angles. It discusses scalene, isosceles, equilateral, acute-angled, right-angled, and obtuse-angled triangles. It also outlines some key properties of triangles, including that they have three sides and three angles, medians connect vertices to midpoints of opposite sides, altitudes are perpendicular from vertices to opposite sides, exterior angles equal the sum of interior opposite angles, and isosceles triangles have equal angles opposite equal sides. The Pythagorean theorem is also summarized.

Introduction To Trigonometry

It is a ppt on Trigonometry for th students of class 10 .
The basic concepts of trigonometry are provided here with examples Hope that that you like it .!! Thankyou ..!! :)

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.

Class IX Heron's Formula

The document discusses Heron's formula for calculating the area of a triangle. Heron's formula uses the lengths of the three sides of a triangle to calculate its area, rather than requiring the base and height. The formula is defined as the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter (half the perimeter) and a, b, c are the three side lengths. The formula is useful when it is difficult to measure the base and height of a triangle directly. An example problem demonstrates calculating the area of a triangle with side lengths 3cm, 4cm, and 5cm using Heron's formula.

Math lecture 8 (Introduction to Trigonometry)

Trigonometry involves calculating relationships between sides and angles of triangles. The main trigonometric functions are sine, cosine, and tangent, which relate the opposite, adjacent, and hypotenuse sides to an angle. These functions repeat in a repeating pattern as angles increase or decrease by full rotations. Trigonometry is used to solve for unknown sides and angles of triangles.

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 Lesson: Introduction & Basics

Trigonometry Lesson: Introduction & Basics

Introduction To Trigonometry

Introduction To Trigonometry

Trigonometry slide presentation

Trigonometry slide presentation

Trigonometry

Trigonometry

Basic trigonometry

Basic trigonometry

Trigonometry

Trigonometry

trigonometry and application

trigonometry and application

Maths ppt on some applications of trignometry

Maths ppt on some applications of trignometry

Trigonometry maths school ppt

Trigonometry maths school ppt

Geometry presentation

Geometry presentation

Trignometry in daily life

Trignometry in daily life

Circles IX

Circles IX

Trigonometry

Trigonometry

Pythagoras And The Pythagorean Theorem

Pythagoras And The Pythagorean Theorem

Triangles and its properties

Triangles and its properties

Introduction To Trigonometry

Introduction To Trigonometry

Trigonometry project

Trigonometry project

Class IX Heron's Formula

Class IX Heron's Formula

Math lecture 8 (Introduction to Trigonometry)

Math lecture 8 (Introduction to Trigonometry)

Trigonometry, Applications of Trigonometry CBSE Class X Project

Trigonometry, Applications of Trigonometry CBSE Class X Project

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 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 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 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.

Maths project trignomatry.pptx

This document presents information about trigonometry. It discusses that trigonometry deals with relationships between sides and angles of triangles, specifically right triangles. It covers the history of trigonometry dating back 4000 years to ancient civilizations. The key trigonometric ratios of sine, cosine, and tangent are defined in relation to a right triangle. Various applications of trigonometry are mentioned, including in fields like construction, astronomy, navigation, and engineering. In conclusion, trigonometry has many useful applications and continues to be an area of ongoing mathematical research.

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.

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.

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.

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.

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.

Maths ppt

Trigonometry has its origins in ancient civilizations over 4000 years ago. It was originally developed to calculate sundials. Key developments include Hipparchus introducing trigonometry tables using the sine function in 150 BC and ancient Indian mathematicians computing trigonometric functions in the Sulba Sutras between 800-500 BC. Trigonometry is the measurement of triangles, derived from Greek words meaning "triangle" and "measure". It involves defining trigonometric ratios like sine, cosine, and tangent that relate the sides of a right triangle to an angle. Trigonometric identities are important relationships between functions that are useful for problem solving.

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

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...........

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.

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.

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

Maths project trignomatry.pptx

Maths project trignomatry.pptx

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Trigonometry class10.pptx

นำเสนอตรีโกณมิติจริง

นำเสนอตรีโกณมิติจริง

Class 10 Ch- introduction to trigonometrey

Class 10 Ch- introduction to trigonometrey

PPT on Trigonometric Functions. Class 11

PPT on Trigonometric Functions. Class 11

Trigonometry

Trigonometry

presentation_trigonometry-161010073248_1596171933_389536.pdf

presentation_trigonometry-161010073248_1596171933_389536.pdf

Maths ppt

Maths ppt

Trigonometry abhi

Trigonometry abhi

Trigonometry Presentation For Class 10 Students

Trigonometry Presentation For Class 10 Students

Trigonometry

Trigonometry

trigonometryabhi-161010073248.pptx

trigonometryabhi-161010073248.pptx

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5th LF Energy Power Grid Model Meet-up Slides

5th Power Grid Model Meet-up
It is with great pleasure that we extend to you an invitation to the 5th Power Grid Model Meet-up, scheduled for 6th June 2024. This event will adopt a hybrid format, allowing participants to join us either through an online Mircosoft Teams session or in person at TU/e located at Den Dolech 2, Eindhoven, Netherlands. The meet-up will be hosted by Eindhoven University of Technology (TU/e), a research university specializing in engineering science & technology.
Power Grid Model
The global energy transition is placing new and unprecedented demands on Distribution System Operators (DSOs). Alongside upgrades to grid capacity, processes such as digitization, capacity optimization, and congestion management are becoming vital for delivering reliable services.
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For the upcoming meetup we are organizing, we have an exciting lineup of activities planned:
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Threats to mobile devices are more prevalent and increasing in scope and complexity. Users of mobile devices desire to take full advantage of the features
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Test Automation with generative AI and Open AI.
UiPath integration with generative AI
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GenAI Pilot Implementation in the organizations

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In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
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“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...

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For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
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The videorecording (in Czech) from the presentation is available here: https://youtu.be/WzjJWm4IyPk?si=SImb06tuXGb30BEH .

Salesforce Integration for Bonterra Impact Management (fka Social Solutions A...

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- 1. Trigonometry MATHS HOLIDAY HOMEWORK MADE BY SRISHTI BHOLA X-A 1
- 2. Trigonometry 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. 2
- 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). 3
- 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 4
- 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 5
- 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 6
- 7. Values of trigonometric function of Angle A sinθ = a/c cosθ = b/c tanθ = a/b cosecθ = c/a secθ = c/b cotθ = b/a 7
- 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 8
- 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. 9
- 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)} 10
- 11. Relation between different Trigonometric Identities • Sine • Cosine • Tangent • Cosecant • Secant • Cotangent 11
- 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. 12
- 13. Problem solved using trigonometric ratios CLICK HERE! 13
- 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. 14
- 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. 15
- 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 . 16
- 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. 17
- 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. 18
- 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. 19
- 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 20