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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 $\cot$.

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Do you know what the graph of $y=\sin x$ looks like? Ditto, $y=\cos x$? From looking at the graphs, you should be able to see how far you have to move one to have it coincide with the other.

Same for the graphs of the other trig functions.

If you don't know what the graphs look like, that's a good place to start.

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    You could work out the addition formula for the tangent from its relation to the sine and cosine, or you could look it up - it's guaranteed to be on the Wikipedia page for the trig functions.2012-05-19