Finding the Current in a Series RLC Circuit
The input voltage is $$V= V_{in}\cos(w t) = V_{in}\angle 0^{\circ}$$
The impedance is 
$$Z=R+\frac{-j}{wC}+jwL=R+j(wL-1/wC) = |Z|\angle\theta$$
Where \$|Z|=\sqrt{R^2+(wL-1/wC)^2}\$ and \$\theta=\tan^{-1}\left(\frac{wL-1/wC}{R}\right)\$.

Then the current will be 
$$I=\frac{V}{Z}=\frac{V_{in}\angle0^{\circ}}{|Z|\angle \theta}=\frac{V_{in}\angle(-\theta)}{|Z|}$$
$$=\frac{V_{in}\cos(wt-\theta)}{\sqrt{R^2+(wL-1/wC)^2}}$$