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

**mlaschansky** · March 15th 2013, 02:50 PM

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

sin 2x =

3

cos x

**Prove It** · March 15th 2013, 02:58 PM

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

**HallsofIvy** · March 15th 2013, 04:39 PM

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?

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