1. Chapter 5 Analytic Trigonometry

2. Intro

6. Using Fundamental Identities Intro In previous chapters, we studied __________ ________________, ______________, ______________, and ______________ of the individual trigonometric functions. In this chapter you will learn how to use the fundamental identities to 1.Evaluate trig functions 2.Simplify trig expressions 3.Develop additional trig identities 4.Solve trig equation basicdefinitionsproperties graphsapplications

7. Trigonometric Identities

10. Co-functions

11. Even and Odd Trig Functions even when we evaluate the negative angle, it is the same as sec ( t ) cos ( t ) the positive angle

12. Even and Odd Trig Functions cont. odd when we evaluate the negative angle, it is the opposite sign as -sin (t) -tan (t) -csc (t) -cot (t) the positive angle

13. Using Fundamental Identities usegiventrig othertrigfunctions

14. Using Fund Identities cont. Sin θθQuadrant III negative negative positive negative

15. Factoring Review Please complete on separate sheet of paper 1.2.3. 4.5.6.

16. Using Fund Identities cont.

19. Example 4 Factoring Trig Expressions Simplify and Factor Csc 2 x – cot x -3 Example 5 Simplifying Trig Expressions Simplify Sin θ + cot θ cos θ

20. Using Fund Identities cont.

21. Factor 1. 3x – 32. xy – y3. 4 – 4x4. z – yz 5. x 2 – x 2 y6. a 2 – a 2 b 2 7. c 2 – c 2 d 2 8. cot 2 – cot 2 cos 2

22. Verifying Trig Identities verifying trigonometric identities trig fundamentalidentitiesalgebra trig expressions

23. GUIDELINES FOR VERIFYING TRIG IDENTITIES

24. Example 1 Verifying Trig Identities

25. As you can see, there can be more than one way to verify an identity. Here is your chance to be creative but as efficient as possible. Example 2 Combining Fractions Before Using Trig Identities Example 3 Verifying a Trig Identity

26. Example 4 Converting to Sines and Cosines Example 5 Verifying a Trig Identity

27. Please pick up and complete the paper in the red tray.

28. Example 6 Working with Each Side Separately

29. Solving Trig Identities 123

30. A similar idea applies when solving trig equations. Example 1 Solving a Trig EquationExample 2 Collecting Like Terms

31. Example 3 Extracting the Square Root

32. Solving Trig Identities two more collecttermsone separate factoring appropriate identities

33. Solving Trig Identities Example 4 FactoringExample 5 Factoring of Quadratic Type

34. Solving Trig Identities Example 6 Rewriting with a Single Trig Function Example 7 Squaring to Convert

35. Solving Trig Identities Example 8 Solving Trig EquationsExample 9 Solving Trig Equations