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1. The problem statement, all variables and given/known data

Hey guys.

cos(n*x) when n is natural and x=pi equals to (-1)^n as I wrote in the pic.

What I'm looking for is the same thing in sinus, lets say again that n is natural, is there a x that can make sinus to behave something like cos? and by that I mean an expression that can be written in on line like (-1)^n (x can be anything).

I hope that was understood.

Thanks in advance.

2. Relevant equations

3. The attempt at a solution

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# Problem with sinus

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