Show $\sin(\frac{\pi}{3})=\frac{1}{2}\sqrt{3}$ I have to show that 
$$\sin\left(\frac{\pi}{3}\right)=\frac{1}{2}\sqrt{3}$$
and 
$$\cos\left(\frac{\pi}{3}\right)=\frac{1}{2}$$
Should I use the exponential function?

Note that:
$sin(3\theta)=3sin(\theta)-4sin^{3}(\theta)$
Let $\theta =\frac{\pi}{3}$ and let $sin(\frac{\pi}{3})=x$
Then:
$0=x(3-4x^{2})$.
Hence either $x=0$ or $x^{2}=\frac{3}{4}$
But since $sin(0)=0$ and the $sine$ function has a period of $2\pi$ then we must conclude that $sin(\frac{\pi}{3})=\frac{\sqrt3}{2}$
