1. Multiple-Angle and Product-Sum Formulas

2. Double-Angle Formulas
sin 2u = 2 sin u cos u
cos 2u = cos 2 u – sin2 u
= 2 cos2 u – 1
= 1 – 2 sin 2 u
tan 2u = 2 tan u
1 – tan2 u

3. Solve 2 cos x + sin 2x = 0 2 cos x ( 1 + sin x) = 0
cos x = 0 or 1 + sin x = 0
x = π/2 + πk

4. Graph y = 4 cos2x – 2
= 2 (2cos2 x – 1)
= 2 cos 2x
Amplitude is 2
Period is π
Now sketch.

5. Power-Reducing Formulas
sin2 u = 1 – cos 2u 2
cos2 u = 1 + cos 2u
tan2 u = 1 – cos 2u
1 + cos 2u

6. Rewrite sin4 x as the first power of cosines.

7. Half-Angle Formulas (Day 2)
sin u/2 = ± √{(1 – cos u)/2}
cos u/2 = ± √{(1 + cos u)/2}
tan u/2 = (1 – cos u)/sin u = sin u / (1 + cos u)