1. 6.2 Cofunction and Double-Angle Identities Fri Dec 5 Do Now Simplify (sinx + cosx)(sinx – cosx)

2. Cofunction Identities

3. Proof These can be proven using the sum and difference identities Proof of sin identity:

4. Cofunction Identities for Sine and Cosine Because of sine and cosine’s relationship, they have 2 more identities

5. Finding other identities Ex: Find an identity for

6. Ex2 Find an identity for

7. Double Angle Identities Double-Angle identities give trig function values of 2x These are also proven using the sum identities

8. Ex Given tanx = -3/4, and x is in quadrant 2, find 1) sin2x 2) cos2x 3) tan2x 4) The quadrant 2x lies in

9. Ex Find equivalent expressions for sin 3x in terms of x

10. Ex Find equivalent expressions of (cosx)^3 in terms of x or 2x, raised only to the first power

11. Closure Find an exact value of sin2x, cos2x, and tan2x if cosx = 5/13 in quadrant 1 HW: p.553 #3-15, 23, 29 33

12. 6.2 Half Angle Identities Mon Dec 8 Do Now Find the exact value of sin2x cos2x and tan2x if tanx = -15/8 in quadrant 2

13. HW Review: p.553 #3-15, 23, 29 33

14. Half-Angle Identities We can find trig functions of angles that are half of what we already know how to find

15. Ex1 Find the exact value of

16. Ex2 Simplify

17. Ex3 Simplify

18. Closure Given sinx = 4/5, evaluate sin (x/2) HW: p.554 #17-21 25 27 31