<s>[INST] 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?
 [/INST] Not to confuse you. But..
$$x=\dfrac{\pi}{3}$$
$$3x=\pi$$
$$\sin 3x=\sin \pi$$
$$3\sin x-4\sin^3x=0$$
$$\sin x=0 \text{ or } \sin x = \dfrac{\sqrt{3}}{2} \text{ or } \sin x = \dfrac{-\sqrt{3}}{2}$$
$$\text{as } 0<\dfrac{\pi}{3}<\dfrac{\pi}{2} \text{, } \sin \dfrac{\pi}{3} = \dfrac{\sqrt{3}}{2}$$
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