1. Examples Double Angle Formulas
Find the exact value of the trig function. 5
1) sin x 3 x 4
2) cos x
x = y = r = 5
3) tan x

2. Examples Double Angle Formulas5
Find the exact value of the trig function. 3 x -4
4) sin 2x
x = y = r = 5
5) cos 2x
6) tan 2x

3. Examples Double Angle Formulas
Find the exact value of the equation in the interval [0 , 2π).
7) sin 2x + cos x = 0
8) sin 2x sin x = cos x
(2 sin x cos x) + cos x = 0
(2 sin x cos x) sin x = cos x
cos x (2 sin x + 1) = 0
2 sin 2 x cos x - cos x = 0
cos x = sin x + 1 = 0
cos x ( 2 sin 2 x - 1) = 0
sin x = -1/2
cos x = sin 2 x - 1 = 0
sin 2 x = 1/2
sin x =

4. Examples Double Angle Formulas
Find the exact value of the equation in the interval [0 , 2π).
9) cos 2x + sin x = 0
sin 2 x + sin x = 0
write in standard form and change all the signs (multiply by -1) to make sin2x a positive # .
2 sin 2 x - sin x - 1 = 0
think of this as
2x2 - x and factor
(2x + 1) (x - 1)
Now put the sin x back in.
(2 sin x + 1) (sin x - 1) = 0
2 sin x + 1 = sin x - 1 = 0
sin x = -1/ sin x = 1