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. 

Just use the sine addition theorem:
$$r \sin{(\omega t-\theta)} = r \sin{\omega t} \, \cos{\theta} - r \cos{\omega t} \, \sin{\theta}$$
Comparing...we get
$$A = r \cos{\theta}$$
$$B = r \sin{\theta}$$
so that
$$r^2 = A^2+B^2$$
$$\theta = \arctan{\frac{B}{A}}$$
