1. Section 5.5 Double Angle Formulas
These angles will be given to you on the test.

2. #1 #2 #3

3. Example 1
Verify the identity

4. Example 2
Verify the identity.
sin 4x = 4 sin x cos x cos 2x

5. sin 4x = 4 sin x cos x cos 2x
sin 2(2x) = 4 sin x cos x cos 2x
2sin 2x cos 2x = 4 sin x cos x cos 2x
2(2 sin x cos x) cos 2x = 4 sin x cos x cos 2x
4 sin x cos x cos 2x = 4 sin x cos x cos 2x

6. Example 3
Solve cos 2x + cos x = 0 in the interval [0, 2).

7. cos 2x + cos x = 0
2cos2 x − 1 + cos x = 0
2cos2 x + cos x − 1 = 0
(2cos x − 1)(cos x + 1) = 0
2cos x − 1 = 0
or cos x + 1 = 0
or cos x = − 1

8. or cos x = − 1

9. Example 4
Use a double angle formula to rewrite the equation g(x) = 3 − 6sin2 x.
g(x) = 3 − 6sin2x
= 3(1 − 2sin2 x)
= 3(cos 2x)

10. Example 5
Hint: Draw “u” in the given quadrant.

11. 5 3 u 4