Intuition for the identity $\sin 3x = \cos\left(3x - \frac{\pi}{2}\right)$

Can someone explain to me in any way why the following is true?

$$\sin 3x = \cos\left(3x - \frac{\pi}{2}\right)$$

I tried to look at the unit circle but I didn't really understand it.

• Look at a right angle triangle not the unit circle. It basically amounts to choosing an angle in the right-triangle and labelling the sides accordingly. I will try to put a more fuller answer when I've chance but I hope it helps. Ditch the $3x$ putting $u=3x$ for simplicity. – Karl Oct 9 '15 at 10:00
• See this answer. – Blue Oct 9 '15 at 10:38
• hint: $\cos\theta = \cos(-\theta)$ – John Joy Oct 9 '15 at 14:28

Because $\sin x=\cos \left( x-\frac\pi 2\right)$
If you want another proof: Use trigonometric identity: $\cos(x-y)=\cos x \cos y+\sin x \sin y$, let $x=3x,y=\frac\pi2$