1. Chapter 7 Section 7.1 Fundamental Identities

2. Trigonometric Relations The six trigonometric functions are related in many different ways. Several of these are quite useful for solving different problems, finding values for the trigonometric functions or solving trigonometric equations. Fundamental Trigonometric Identities: ( They form the building blocks for many other identities. ) Reciprocal Identities: Pythagorean Identities: Even/Odd Identities: Co-function Identities:

3. Simplifying Trigonometric Expressions It is often useful to be able to simplify a trigonometric expression. For example, when you are trying to solve an equation that involves trigonometric functions. There are many ways to do this but the two that are used very often are: 1. Change to sines and cosines. 2. Combine fractions and expressions where possible. Here are some examples. (Notice these are expressions! (i.e. there is no equal sign).) Simplify

4. Reciprocal Pythagorean

5. Substitute back: