1. Chapter 5.1

2. 5.1 Using Fundamental Identities In this chapter, you will learn how to use the fundamental identities to do the following: Evaluate trigonometric functions Simplify trigonometric expressions Develop additional trigonometric identities Solve trigonometric equations

3. 5.1 Using Fundamental Identities Using Identities to evaluate a function Why should you learn this? In calculus you will use trigonometric identities to simplify an expression. Ex: Homework p.347 #97 is an example

4. 5.1 Using Fundamental Identities Quadrant II Quadrant IVQuadrant III Quadrant I

5. 5.1 Using Fundamental Identities Using Identities to Evaluate a Function Given: Find: The value of all six trigonometric functions *Remember: Once you know the value of Sine and Cosine you can find the values of all six trigonometric functions

6. 5.1 Using Fundamental Identities Given: *Use the information given to decide which quadrant Which quadrant are we in? 1 ______ Find: The value of all six trigonometric functions Looking at page 340 in your book: Can you see which identity we should use to find the value of sine?

7. 5.1 Using Fundamental Identities Pythagorean Identity 2

8. 5.1 Using Fundamental Identities Now we know 3 :

9. 5.1 Using Fundamental Identities Now try #11 pg.345 4

10. 5.1 Using Fundamental Identities Simplifying a Trigonometric Expression 5 Factor out a Use the distributive property Use the Pythagorean Identity Multiply

11. 5.1 Using Fundamental Identities Verifying a Trigonometric Identity 7

12. 5.1 Using Fundamental Identities Now try #45 pg.346 8 To check graphically, use radian mode graph one side of the equation as and the other side of the equation as. (Select line style for and path style for. )

13. 5.1 Using Fundamental Identities Factoring Trigonometric Expressions 9 a.) b.)

14. 5.1 Using Fundamental Identities Now try #51 pg.346 10

15. 5.1 Using Fundamental Identities *NOTE: On occasion, factoring or simplifying can best be done by rewriting the expression in terms of just one trigonometric function or in terms of sine or cosine alone. Simplify 11 :

16. 5.1 Using Fundamental Identities Now try #67 pg.346 12

17. 5.1 Using Fundamental Identities Enriched Pre-Calculus Rewriting a Trigonometric Equation Rewrite 13 so that it is not in fractional form.

18. 5.1 Using Fundamental Identities Now try #69 pg.346 14

19. 5.1 Using Fundamental Identities Enriched Pre-Calculus Trigonometric Substitutions 15 Use the substitution to write as a trigonometric function of.

20. 5.1 Using Fundamental Identities Now try #81 pg.347 16

21. THE END