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So, previously in my math classes I have been taught that The phase shift of $\sin(ax+c)$ is c.

But in my new class they say that $ \sin(ax+c) = \sin(a(x+c))$ which I believe to be wrong. But I have an exam tommorrow and I do not wish to be marked down for having the wrong phase shift.

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    Okay, Well thank you.2012-10-22

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There seem to be different conventions about phase shift. See this Regents link, where it says that if $y=\sin(2x-(\pi/2))=\sin(2(x-(\pi/4)))$ then physicists and engineers say the phase shift is $\pi/2$ but some math textbooks say it's $\pi/4$. Find out for certain which convention your class is using, and use it. If it's too late for that, then declare which convention you are using, and stick with it.