Question

for interval [0,2π) solve cos(4x)=1/2

Answer 1

4x =arccos(1/2)

Answer 2

x= pi/12

Answer 3

+πk/2

k=0,1,2,3?

Answer 4

wait we need to continue

Answer 5

(0,2pi), now we know that cos is positive in in the first and forth quarter

Answer 6

First solve \(\cos(\theta)=1/2, \theta\in [0,2\pi)\)

Answer 7

This is an easy angle.
Actually \(\theta \in [0,8\pi)\)

So we have \(\theta = \pi/3,\theta = 2\pi - \pi/3,...\)

Answer 8

\[
\theta = \{\pi/3,5\pi/3,7\pi/3,11\pi/3,13\pi/3,17\pi/3,19\pi/3,23\pi/3\}
\]Now \[
4x = \theta \implies x = \theta/4
\]So divide all those solutions by 4