Write $5 \cos \theta+(75)^{1 / 2} \sin \theta$ in the form $R\sin(\theta+\varepsilon)$, $R>0$

Question

What is this topic called , as in what should I read inorder to be able to answer this. I know its some form of trig identity but I think these have a specific name

Answer 1

All you need to know is the formula for $\sin(x+y)$

$$5\cos\theta+(75)^{1/2}\sin\theta=5\cos\theta+5\sqrt 3\sin\theta=10(\frac 12\cos\theta+\frac{\sqrt 3}2\sin\theta)=10(\sin\frac\pi 6\cos\theta+\cos\frac\pi 6\sin\theta)$$

Can you take it from here?