In the trigonometric identity $\cos(\frac{\pi}{2} -\theta)$, why are we reflecting the graph in vertical axis. I was wondering why do we need to reflect the graph in vertical axis in the trigonometric identity: 

$\cos(\frac{\pi}{2} -\theta) = \sin(\theta)$.

It seems that if we only translate the graph of $\cos(\theta)$ by $\frac{\pi}{2}$ it would take the same values as the graph of $\sin(\theta)$, so why do we reflect the graph by changing sign of $\theta$ to negative.

Hint:$$\cos(-x)=\cos(x)$$Cosine is even and that is one of the properties of an even function.
Note that $$\cos(\frac{\pi}2+\theta)\ne\sin(\theta)$$
