Encyclopedia of Trigonometry.pdf

First Edition, 2007

ISBN 978 81 89940 01 0

Published by:

Global Media

1819, Bhagirath Palace,

Chandni Chowk, Delhi-110 006

Email: globalmedia@dkpd.com

Table of Contents

1. Introduction

2. In Simple Terms

3. Radian and Degree Measure

4. Trigonometric Angular Functions

5. Right Angle Trigonometry

6. Properties of the Cosine and Sine Functions

7. Taylor Series Approximations for the Trig. Functions

8. Inverse Trigonometric Functions

9. Applications and Models

10. Verifying Trigonometric Identities

11. Solving Trigonometric Equations

12. Sum and Difference Formulas

13. Additional Topics in Trigonometry

14. Solving Triangles

15. Vectors in the Plane

16. Trigonometric Identities

17. History of Trigonometry

18. Common Formulae

19. Exact Trigonometric Constants

20. Pythagorean Theorem

Trigonometry

Introduction

Trigonometery is the study of triangles. “Tri” is Ancient Greek word for three,

“gon” means side, “metry” measurementtogether they make “measuring

three sides”. If you know some facts about a triangle, such as the lengths of

it sides, then using trignometry you can find out other facts about that

triangleits area, its angles, its center, the size of the largest circle that can be

drawn inside it. As a consequencethe Ancient Greeks were able to use

trigonometery to calculate the distance from the Earth to the Moon.

Trigonometry starts by examining a particularly simplified trianglethe right-

angle triangle. More complex triangles can be built by joining right-angle

triangles together. More complex shapes, such as squares, hexagons, circles

and ellipses can be constructed from two or more triangles. Ultimately, the

universe we live in, can be mapped through the use of triangles.

Trigonometry is an important, fundamental step in your mathematical

education. From the seemingly simple shape, the right triangle, we gain tools

and insight that help us in further practical as well as theoretical endeavors.

The subtle mathematical relationships between the right triangle, the circle,

the sine wave, and the exponential curve can only be fully understood with a

firm basis in trigonometry.

Trigonometry is a system of mathematics, based generally on circles and

triangles, that is used to solve complex problems (again, mainly involving

circles and triangles). Extensions of various algebraic formulas, namely the

Pythagorean theorem, are utilized.

In Review

Here are some useful formulas that should be learned before delving into

trigonometry:

Pythagorean Theorem a 2 + b 2 = c 2 , in a right triangle where a and b are the two sides,

and c is the hypotenuse.

Pythagorean Triples3-4-5 (the two smaller values being the sides, with the larger the

hypotenuse), 5-12-13, 7-24-25, 8-15-17, and any multiples of these (including 6-8-10,

10-24-26, etc.)

Properties of Special Right Triangles

In a 45-45-90 right triangle, i.e., an isosceles right triangle, let one leg be x.

The hypotenuse is then x In a 30-60-90 right triangle, let the short leg,

i.e. the leg opposite the 30° angle, be x. The hypotenuse is then equal to 2x

and the longer leg, i.e. the leg opposite the 60° angle, is equal to x* .

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