1. Trigonometric Identities Putting the Puzzle Pieces Together

2. Establishing Identities Two functions f and g are said to be identically equal if f(x) = g(x) for every value of x for which both functions are defined. Such an equation is referred to as an identity.

3. Establishing an Identity Use the basic trig identities to establish the identity csc θ tan θ = sec θ

4. Guidelines for Establishing Identity 1. Start with the side containing the more complicated expression 2. Rewrite sums or differences of quotients as a single quotient 3. Sometimes, rewriting one side in terms of sines and cosines only will help 4. Always keep your goal in mind. Keep looking at the other side of the equation as you work

5. Establishing an Identity Establish the identity

6. Guidelines for Establishing Identities Be careful not to handle like an equation. You cannot establish an identity by such methods as adding the same expression to each side and obtaining a true statement.

7. Establishing an Identity Establish the identity

8. Establishing an Identity Establish the identity

9. Solution

10. Establishing an Identity Establish the identity

11. Solution

12. Establishing an Identity Establish the identity

13. Solution

14. Establishing Inverse Trig Identities

15. Establishing Trig Identities Many more examples on pgs. 478 – 479 On-line examples

16. Solution

17. Establishing Inverse Trig Identities Show that

18. Solution

19. One Last Toughie Establish the identity