Trigonometry and differential equations I have the expression $A\cos(wt)+B\sin(wt)$ and I need to write it in the form $r\sin(wt−\theta)$. 
I then have to determine $r$ and $\theta$ in terms of $A$ and $B$. If $R\cos(wt - \delta) = r\sin(wt - \theta)$, determine the relationship among $R, r, \theta,$ and $\delta$.
I think $R=r$, but I'm a bit stuck. 

You are correct that
$R = r$.
This is implied by the fact that
the extreme values of
$\sin$ and $\cos$
are $\pm 1$.
For your first expression,
expand
$r\sin(wt−\theta)$
using the formula for
$\sin(x+y)$,
equate the result to
$A\cos(wt)+B\sin(wt)$,
and see what you get
for $A$ and $B$
in terms of
$r$ and
$\theta$.
