Right the question is hence or otherwise, find the time taken for each blade to complete one revolution.
$h(t) = 65+36\sin(3/2t)-15\cos(3/2t)$
I guess you'd divide $2\pi/(3/2)$ and get $4/3 \pi$
Is that the answer, I'm not really to sure as I've never dealt with a sine and cosine function together.
Yes, you are right.
Your height is a periodic function of the time. You are looking for the period of this periodic function.
You see, the $\sin$ and the $\cos$ in your height function are linked together by addition or subtraction and have the same argument. That means, your height function has the same period as this $\sin$ and $\cos$. And you know, the period of the sinus function and of the cosinus function is $2\pi$. That means, the value of this functions are repeated all $2\pi$.
But you wants not the period, you wants the corresponding time. The period of the height function is $\frac{3}{2}t=2\pi$. The result is $t=\frac{4}{3}\pi$ s.