Working on the angle functions, there's a problem that says:
Determine the angle needed to slide the $\cos$ curve into the $\sin$ curve.
The solution is described as
$\cos\Big(x - \dfrac{\pi}{2}\Big) = \sin(x)$
Which means, the needed angle is $-\dfrac{\pi}{2}$.
How do I know (or calculate) that particular angle?
And how do I do the same when determining the angle needed to slide one curve of any angle function to any curve of any other angle function?
The functions I know of are $\sin$, $\cos$, $\tan$ and $\cot$.