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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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1 Answer

up vote 1 down vote accepted

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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That's true, hadn't thought of that. But I was wondering how you would find it out without a graph. –  Miroslav Cetojevic May 19 '12 at 12:41
    
Without a graph? Well. do you know the addition formulas, $\sin(a+b)=\sin a\cos b+\cos a\sin b$ and the like? If you want just $\cos a$ on the right you have to take $b$ so the $\cos b$ on the right goes away, so take $b=\pi/2$, so $\sin(a+(\pi/2))=\cos a$. Alternatively, do you know the definitions of the trig functions in terms of points on the unit circle? –  Gerry Myerson May 19 '12 at 12:47
    
Without a graph? Well. do you know the addition formulas, $\sin(a+b)=\sin a\cos b+\cos a\sin b$ and the like? If you want just $\cos a$ on the right you have to take $b$ so the $\cos b$ on the right goes away, so take $b=\pi/2$, so $\sin(a+(\pi/2))=\cos a$. Alternatively, do you know the definitions of the trig functions in terms of points on the unit circle? –  Gerry Myerson May 19 '12 at 12:50
    
No, didn't know about those formulas. How do they apply to the other functions ($\tan$ and $\cot$)? Maybe you could expand on that in your answer? About the unit circle, I got some notion of how that works, but I'm not entirely comfortable there. –  Miroslav Cetojevic May 19 '12 at 12:57
    
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. –  Gerry Myerson May 19 '12 at 13:21
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