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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.

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Trigonometry slide presentation

Trigonometry slide presentation

trigonometry and application

trigonometry and application

Basic trigonometry

Basic trigonometry

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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 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.

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.

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 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.

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.

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.

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.

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.

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.

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

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.

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

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

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.

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.

The Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It was named after the Greek mathematician Pythagoras, who lived in the 6th century BC. The theorem can be used to calculate unknown side lengths in right triangles. Some examples are also given to demonstrate applying the theorem.

Ppt on trigonometric functions(For class XI 2020-21)

Trigonometry refers to measuring the sides of a triangle. The word comes from the Greek words 'trigon' meaning triangle and 'metron' meaning measurement. Radian is a unit used to measure angles, where one radian is equal to the central angle that cuts off an arc equal in length to the radius of a circle.

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

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 slide presentation

Trigonometry slide presentation

trigonometry and application

trigonometry and application

Basic trigonometry

Basic trigonometry

Introduction of trigonometry

Introduction of trigonometry

trigonometry and applications

trigonometry and applications

Mathematics ppt on trigonometry

Mathematics ppt on trigonometry

Trigonometry presentation

Trigonometry presentation

Math lecture 8 (Introduction to Trigonometry)

Math lecture 8 (Introduction to Trigonometry)

Class 10 Ch- introduction to trigonometrey

Class 10 Ch- introduction to trigonometrey

Maths ppt on some applications of trignometry

Maths ppt on some applications of trignometry

Introduction To Trigonometry

Introduction To Trigonometry

Trigonometry

Trigonometry

Trigonometry abhi

Trigonometry abhi

Introduction to trigonometry

Introduction to trigonometry

Ppt on trignometry by damini

Ppt on trignometry by damini

Trigonometry Lesson: Introduction & Basics

Trigonometry Lesson: Introduction & Basics

The Pythagorean Theorem

The Pythagorean Theorem

Ppt on trigonometric functions(For class XI 2020-21)

Ppt on trigonometric functions(For class XI 2020-21)

Trigonometry, Applications of Trigonometry CBSE Class X Project

Trigonometry, Applications of Trigonometry CBSE Class X Project

Introduction to trigonometry

Introduction to trigonometry

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.

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.

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

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 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 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 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.

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 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.

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.

Heights & distances

Trigonometry deals with calculating distances and heights using mathematical techniques. It originated in ancient Greece and Egypt for purposes like astronomy and geography. Hipparchus is considered one of the founders of trigonometry for developing quantitative models of celestial motions. Trigonometry is now widely used in fields like calculus, physics, engineering, and more. It allows calculating inaccessible lengths like heights and widths using angles of elevation, depression, and trigonometric functions like sine, cosine, and tangent.

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.

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.

Trigonometric Functions

Trigonometry is the branch of mathematics that deals with relationships between the sides and angles of triangles, especially right triangles. It has been studied since ancient times by civilizations like Egypt, Mesopotamia, and India. Key concepts in trigonometry include trigonometric functions like sine, cosine, and tangent that relate ratios of sides of a right triangle to an angle of the triangle. Trigonometry has many applications in fields like astronomy, navigation, engineering, and more.

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. It defines trigonometric functions that describe these relationships and are applicable to cyclical phenomena like waves. Trigonometry has its origins in ancient Greek and Indian mathematics and was further developed by Islamic mathematicians. It is the foundation of surveying and has many applications in fields like astronomy, music, acoustics, and more.

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. It defines trigonometric functions that describe these relationships and are applicable to cyclical phenomena like waves. Trigonometry has its origins in ancient Greek and Indian mathematics and was further developed by Islamic mathematicians. It is the foundation of surveying and has many applications in fields like astronomy, music, acoustics, and more.

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. It defines trigonometric functions that describe these relationships and are applicable to cyclical phenomena like waves. Trigonometry has its origins in ancient Greek and Indian mathematics and was further developed by Islamic mathematicians. It is the foundation of surveying and has many applications in fields like astronomy, music, acoustics, and more.

Applications of trigonometry

Trigonometry was invented by ancient Greeks to calculate distances and angles in astronomy. It relates the angles and lengths of triangles, allowing unknown values to be determined if one angle and one length are known. Some early applications included creating trigonometric tables for astronomical computations and using triangulation to measure heights and distances. Modern uses include navigation, surveying, engineering, acoustics, and technologies like GPS which rely on trigonometric calculations.

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.

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

Trigonometry

Trigonometry project

Trigonometry project

Maths ppt

Maths ppt

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

PPT on Trigonometric Functions. Class 11

PPT on Trigonometric Functions. Class 11

Trigonometry class10.pptx

Trigonometry class10.pptx

Trigonometry

Trigonometry

Heights & distances

Heights & distances

Maths project trignomatry.pptx

Maths project trignomatry.pptx

presentation_trigonometry-161010073248_1596171933_389536.pdf

presentation_trigonometry-161010073248_1596171933_389536.pdf

Trigonometric Functions

Trigonometric Functions

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Applications of trigonometry

Applications of trigonometry

นำเสนอตรีโกณมิติจริง

นำเสนอตรีโกณมิติจริง

trigonometryabhi-161010073248.pptx

trigonometryabhi-161010073248.pptx

BÀI TẬP BỔ TRỢ 4 KỸ NĂNG TIẾNG ANH LỚP 12 - GLOBAL SUCCESS - FORM MỚI 2025 - ...

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matatag curriculum education for Kindergarten

for educational purposes only

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How to Manage Early Receipt Printing in Odoo 17 POS

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Configuring Single Sign-On (SSO) via Identity Management | MuleSoft Mysore Me...

Configuring Single Sign-On (SSO) via Identity Management | MuleSoft Mysore Me...MysoreMuleSoftMeetup

Configuring Single Sign-On (SSO) via Identity Management | MuleSoft Mysore Meetup #48
Event Link:- https://meetups.mulesoft.com/events/details/mulesoft-mysore-presents-configuring-single-sign-on-sso-via-identity-management/
Agenda
● Single Sign On (SSO)
● SSO Standards
● OpenID Connect vs SAML 2.0
● OpenID Connect - Architecture
● Configuring SSO Using OIDC (Demo)
● SAML 2.0 - Architecture
● Configuring SSO Using SAML 2.0 (Demo)
● Mapping IDP Groups with Anypoint Team (Demo)
● Q & A
For Upcoming Meetups Join Mysore Meetup Group - https://meetups.mulesoft.com/mysore/YouTube:- youtube.com/@mulesoftmysore
Mysore WhatsApp group:- https://chat.whatsapp.com/EhqtHtCC75vCAX7gaO842N
Speaker:-
Vijayaraghavan Venkatadri:- https://www.linkedin.com/in/vijayaraghavan-venkatadri-b2210020/
Organizers:-
Shubham Chaurasia - https://www.linkedin.com/in/shubhamchaurasia1/
Giridhar Meka - https://www.linkedin.com/in/giridharmeka
Priya Shaw - https://www.linkedin.com/in/priya-shawThe Cruelty of Animal Testing in the Industry.pdf

PDF presentation

Lecture_Notes_Unit4_Chapter_8_9_10_RDBMS for the students affiliated by alaga...

Title: Relational Database Management System Concepts(RDBMS)
Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : DATA INTEGRITY, CREATING AND MAINTAINING A TABLE AND INDEX
Sub-Topic :
Data Integrity,Types of Integrity, Integrity Constraints, Primary Key, Foreign key, unique key, self referential integrity,
creating and maintain a table, Modifying a table, alter a table, Deleting a table
Create an Index, Alter Index, Drop Index, Function based index, obtaining information about index, Difference between ROWID and ROWNUM
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.
Feedback and Contact Information:
Your feedback is valuable! For any queries or suggestions, please contact muruganjit@agacollege.in

BRIGADA ESKWELA OPENING PROGRAM KICK OFF.pptx

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Conducting exciting academic research in Computer Science

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Read the 38 letters Rockefeller left to his son online for free

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In Odoo Inventory, packaging is a simple concept of holding multiple units of a specific product in a single package. Each specific packaging must be defined on the individual product form.

Bedok NEWater Photostory - COM322 Assessment (Story 2)

COM322 Assessment - Story 2

How to Empty a One2Many Field in Odoo 17

This slide discusses how to delete or clear records in an Odoo 17 one2many field. We'll achieve this by adding a button named "Delete Records." Clicking this button will delete all associated one2many records.

How to Create & Publish a Blog in Odoo 17 Website

A blog is a platform for sharing articles and information. In Odoo 17, we can effortlessly create and publish our own blogs using the blog menu. This presentation provides a comprehensive guide to creating and publishing a blog on your Odoo 17 website.

(T.L.E.) Agriculture: Essentials of Gardening

(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏.𝟎)-𝐅𝐢𝐧𝐚𝐥𝐬
Lesson Outcome:
-Students will understand the basics of gardening, including the importance of soil, water, and sunlight for plant growth. They will learn to identify and use essential gardening tools, plant seeds, and seedlings properly, and manage common garden pests using eco-friendly methods.

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How to Create & Publish a Blog in Odoo 17 Website

(T.L.E.) Agriculture: Essentials of Gardening

(T.L.E.) Agriculture: Essentials of Gardening

- 1. TRIGONOMETRY
- 2. What is trigonometry? Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees. Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure).
- 3. History of trigonometry• 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. In a right triangle, the shorter sides are called legs and the longest side (which is the one opposite the right angle) is called the hypotenuse First let’s look at the three basic functions. SINE They are abbreviated using their first 3 letters COSINE TANGENT hypotenuse opposite sin hypotenuse adjacent cos adjacent opposite tan
- 5. 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. Easy way to learn trigonometric ratios
- 7. Values of Trigonometric function0 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. Trigonometric ratios of complementary angles • Sin(90-A)= cos A, Cos(90- A)= sin A • Tan(90-a)= cot A, Cot(90-A)= tan A • Sec(90-A)= cosec A, cosec(90-A)= sec A
- 9. Trigonometric identities• Identity1- sin2A + cos2A = 1 • PROOF: • IN TRIANGLE ABC, • AB2 + BC2 = AC2 ( BY PYTHAGORAS THEOREM) (1) • DIVIDING EACH TERM OF (1) BY AC AB2 / AC2 + BC2 / AC2 = AC2 / AC2 (cos A) 2 + (sin A) 2 = 1 → cos2 A + sin2 A = 1 A B C 2
- 10. • Identity2 : 1 + tan2A = sec2A • Dividing eq (1) by AB2 (AB/AB) 2 + (BC/AB2 =(AC/AB) 2 => 1+ Tan2 A = sec2 A • Identity3: 1 + cot2A = cosec2A • Dividing eq (1) by BC2 • (AB/BC) 2 + (BC/BC) 2 = (AC/BC) 2 • => Cot2A + 1 = cosec2 A
- 11. Solving a Problem with the Tangent Ratio 60º 53 ft h = ? 1 2 3 We know the angle and the side adjacent to 60º. We want to know the opposite side. Use the tangent ratio: ft92353 531 3 53 60tan h h h adj opp
- 12. 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, num ber theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, econ omics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography
- 13. 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 .
- 14. Application of Trigonometry in ArchitectureMany 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.
- 15. Thank you Made by- Divya pandey X-A