
Trig Function
How to solve this trig function $\displaystyle 2cos(3x)=1$ for all the values of x: $\displaystyle \frac{\pi}{6}\leq{x}\leq\frac{5\pi}{6}$
can someone please demonstrate how would I solve such problems step by step? I'm still trying to get my head around these trig functions.

$\displaystyle 2cos(3x)=1$
$\displaystyle cos(3x)= \frac{1}{2} $
$\displaystyle cos^{1}(cos(3x)) = cos^{1}(\frac {1}{2}) $
$\displaystyle 3x = cos^{1}( \frac {1}{2}) $
You want to find the angle (or angles) in the range given whose cosine is 1/2. There are two angles: $\displaystyle \frac{\pi}{3}$ and $\displaystyle \frac{\pi}{3} $
so $\displaystyle 3x = \pm \frac{\pi}{3} $
or $\displaystyle x = \pm \frac{\pi}{9} $

Dont forget that if possible the angle may be +or 2*pi within the domain