Chapter 4.4, Problem 16P

Show that $A\cos {\omega }_{0}t+B\sin {\omega }_{0}t$ can be written in the form $r\sin \left({\omega }_{0}t-\theta \right)$. Determine $r$ and $\theta$ in terms of $A$ and $B$. If $R\cos \left({\omega }_{0}t-\delta \right)=r\sin \left({\omega }_{0}t-\theta \right)$, determine the relationship among $R,r,\delta$ and $\theta$.