Confused with Trigonometry Manipulation $$h(t)=65+36\sin(1.5t)-15\cos(1.5t)$$
Can also be written as:
$$h(t)=65+k\sin(1.5t-\alpha)$$ where k and $\alpha$ are unkwowns.
In the marking scheme it says that I can let: $$k\sin\theta=36$$ and $$k\cos\theta=15$$
I am confused as to why we can do this.

All points $(k\sin(\theta),k\cos(\theta))$ are on a cirle with radius $k$.
Because $(36,15)$ lies on this circle you find $k=\sqrt{36^2+15^2}=39$. You find $\theta$ using $36=39\sin(\theta) \Rightarrow \theta \approx 67.38°$.
