1. Precalculus Fifth Edition Mathematics for Calculus James Stewart Lothar Redlin Saleem Watson

2. Trigonometric Identities 7.1

3. Fundamental Trigonometric Identities Reciprocal Identities

4. Fundamental Trigonometric Identities Pythagorean Identities sin 2 x + cos 2 x = 1 tan 2 x + 1 = sec 2 x 1 + cot 2 x = csc 2 x

5. Fundamental Trigonometric Identities Even-Odd Identities sin( – x) = – sin x cos( – x) = cos x tan( – x) = – tan x

6. Simplifying Trigonometric Expressions

7. Identities enable us to write the same expression in different ways. It is often possible to rewrite a complicated looking expression as a much simpler one.

8. Simplifying Trigonometric Expressions To simplify algebraic expressions, we used: Factoring Common denominators Special Product Formulas

9. Simplifying Trigonometric Expressions To simplify trigonometric expressions, we use these same techniques together with the fundamental trigonometric identities.

10. E.g. 1—Simplifying a Trigonometric Expression Simplify the expression cos t + tan t sin t We start by rewriting the expression in terms of sine and cosine.

11. E.g. 1—Simplifying a Trigonometric Expression

12. E.g. 2—Simplifying by Combining Fractions Simplify the expression We combine the fractions by using a common denominator.

13. E.g. 2—Simplifying by Combining Fractions

14. More Examples: Simplify:

15. More Examples: Simplify:

16. Derivatives of trigonometric functions Find and simplify: