# Math Help - Need to find all values of X in the interval [0, 2pi]

1. ## Need to find all values of X in the interval [0, 2pi]

Find all values of X in the interval [0,2pi]

sin 2x =
 3
cos x

2. ## Re: Need to find all values of X in the interval [0, 2pi]

I can't read your equation. Is it \displaystyle \begin{align*} \sin{(2x)} = \sqrt{3}\,\cos{(x)} \end{align*}?

3. ## Re: Need to find all values of X in the interval [0, 2pi]

Assuming that it is $sin(2x)= \sqrt{3}cos(x)$, use a trig identity: $sin(2x)= 2sin(x)cos(x)= \sqrt{3}cos(x)$ one solution is cos(x)= 0 which gives $x= \pi/2$. If cos(x) is NOT 0, we can divide both sides to get $2sin(x)= \sqrt{3}$ so that $sin(x)= \frac{\sqrt{3}}{2}$. Can you solve that?