1. 5.5 Multiple-Angle and Product-Sum Formulas

2. Find all solutions in

3. Sketch the graph of y = 4 cos 2 x - 2 over = 2(2 cos 2 x - 1) = 2 cos 2x

4. Use the fact that to find sin 2x, cos 2x, and tan 2x sin 2x = 2 sin x cos x = cos 2x = 2 cos 2 x - 1 = tan 2x = -12 5 13

5. Express sin 3x in terms of sin x. sin 3x = sin (2x + x) = sin 2x cos x + cos 2x sin x = 2 sin x cos x cos x + (1 - 2 sin 2 x) sin x = 2 sin x cos 2 x + sin x - 2 sin 3 x = 2 sin x(1 - sin 2 x) + sin x - 2 sin 3 x = 2 sin x - 2 sin 3 x + sin x - 2 sin 3 x = 3 sin x - 4 sin 3 x

6. Rewrite sin 4 x as a sum involving first powers of cos x sin 4 x = (sin 2 x) 2 Foil

7. Find the exact value of sin 105 o sin 105 o = sin of 105 is positive

8. Writing Products as Sums Rewrite cos 5x sin 4x as a sum or difference. cos 5x sin 4x =

9. Using a Sum-to-Product Formula Find the exact value of cos 195 0 + cos 105 0 cos 195 0 + cos 105 0 = 2 cos 150 0 cos 45 0

10. Solving a Trigonometric Equation Find all solutions of sin 5x + sin 3x = 0 in 2sin 4x cos x = 0 sin 4x = 0 cos x = 0 Plug in 0, 1, 2, and 3