# Question #d5864

May 19, 2017

pi/8; (3pi)/8; (5pi)/8; (7pi)/8; (9pi)/8; (11pi)/8; (13pi)/8; (15pi)/8

#### Explanation:

cos 4x = 0
The unit circle gives 2 solutions:
$4 x = \frac{\pi}{2}$, and $4 x = \frac{3 \pi}{2}$.
a. $4 x = \frac{\pi}{2} + 2 k \pi$
$x = \frac{\pi}{8} + \frac{k \pi}{2}$
b. $4 x = \frac{3 \pi}{2} + 2 k \pi$
$x = \frac{3 \pi}{8} + \frac{k \pi}{2}$
8 answers for $\left[0 , 2 \pi\right]$ --> k = 0, 1, 2, 3,
k = 0 --> $x = \frac{\pi}{8}$;
k = 1 --> $x = \frac{\pi}{8} + \frac{\pi}{2} = \frac{5 \pi}{8}$;
k = 2 --> $x = \frac{\pi}{8} + \pi = \frac{9 \pi}{8}$,
k = 3 --> $x = \frac{\pi}{8} + \frac{3 \pi}{2} = \frac{13 \pi}{8}$
k = 0 --> $x = \frac{3 \pi}{8}$;
k = 1 --> $x = \frac{3 \pi}{8} + \frac{\pi}{2} = \frac{7 \pi}{8}$
k = 2 --> $x = \frac{3 \pi}{8} + \pi = \frac{11 \pi}{8}$;
k = 3 --> $x = \frac{3 \pi}{8} + \frac{3 \pi}{2} = \frac{15 \pi}{8}$