Sine or Cosine?

Every sine or cosine wave can be written both ways. The wave with a top at 0 is $y = 2\cos\left(x\right)$, and it is also $y = 2\sin\left(x+\frac{\pi}{2}\right)$: the same curve. Which one to write depends on what the question asks for, and on what is simplest.

Look at x = 0. If the wave is at a top or a bottom there, a cosine needs no shift: a top means a positive a, a bottom a negative a. If it is on its midline there, a sine needs no shift: going up means a positive a, going down a negative a.

If the question asks for the other function, you need a shift to make it fit.