Solving Trig Function with both $\sin$ and $\cos$ I am trying to understand the function $h(t) = 65 + 36\sin\left(\frac{3t}{2}\right) - 15\cos\left(\frac{3t}{2}\right)$, where $t$ is the time in seconds and $\frac{3t}{2}$ is expressed in radians.
A question asks that I find the times in the first revolution when the height is exactly $65$m. Using basic algebra I have been able to solve in order to get time which is $t = 0.26319$. But the question asks for times in the first revolution and I am having trouble understanding how to find these values.
Hence, I need to find the time to complete one revolution and the angular speed of the function. 
How would you determine the times when the height is $65$m and from that be able to determine the time it takes to complete one revolution and the angular speed of the function?
I assume that this equation is not in the form of $a + b\sin(cx)$?

Hint
use $${a\over \sqrt{a^2+b^2}}\cos u+{b\over \sqrt{a^2+b^2}}\sin u=\cos(u-\theta)$$where$$\theta =\cos^{-1}{a\over \sqrt{a^2+b^2}}=\sin^{-1}{b\over \sqrt{a^2+b^2}}$$
