We need to get this in a simpler form. In this one, notice that the angles in the brackets are not the same!

We must simplify them first so they are the same.

Now we can express i in the form R sin(t + α).

So

2 sin t − 1.732 cos t = 2.646 sin(t − 0.714)

So the maximum value of this is 2.646 A.

To find when this occurs, we need to solve:

2.646 sin(t − 0.714) = 2.646

i.e. sin(t − 0.714) = 1

t − 0.714 = π/2

t = 2.29

So t = 2.29 s is the time when the maximum is first reached.