1. ## Trig Function

How to solve this trig function $2cos(3x)=1$ for all the values of x: $\frac{-\pi}{6}\leq{x}\leq\frac{5\pi}{6}$

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.

2. $2cos(3x)=1$

$cos(3x)= \frac{1}{2}$

$cos^{-1}(cos(3x)) = cos^{-1}(\frac {1}{2})$

$3x = cos^{-1}( \frac {1}{2})$

You want to find the angle (or angles) in the range given whose cosine is 1/2. There are two angles: $\frac{\pi}{3}$ and $-\frac{\pi}{3}$

so $3x = \pm \frac{\pi}{3}$

or $x = \pm \frac{\pi}{9}$

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