Q:

When to use sine or cosine when computing simple harmonic motion

For simple harmonic motion (SHM), I am aware you can start of using either sine or cosine, but I am a bit confused as to when you would start off with sine rather than cosine. I know that a sine graph starts at $y=0$ and a cosine graph starts at $y=1$. So therefore, I would say you use sine for equilibrium positions? 
However, I came across a question asking to write down the equations for position, velocity and acceleration of a particle starting from rest at time $t=0$, then undergoing SHM with maximum amplitude 0.2 m and period 5 sec.
I worked out the angular frequency to be $2\pi/5$ from the period formula. And then used the position formula to be of the form with sine and differentiated to get cosine velocity equation, etc. However, the answer says I should have started with cosine and I am now unsure when I should start with sine or cosine. 

A:

The function $x(t) = A \sin \omega t$ starts from zero with maximum speed, while the function $x(t) = A \cos \omega t$ starts from $x=A$ (the amplitude) with zero speed, and starts to move towards $x=0$. Starting from rest doesn't imply starting at the equilibrium position: if you start from rest at $x=0$, nothing moves, so this is not an interesting solution! For a harmonic oscillator, starting from rest means starting at the maximum value of $x$, so $\cos \omega t$ is the appropriate solution.

