Chapter 4, Problem 4.2HP

For each case shown below, derive the expression forthe current through a $200\text{-}\mu F$ capacitor. $v_C\left(t\right)$ is thevoltage across the capacitor.
a. $v_C\left(t\right)=22\cos \left(20t-\frac{\pi }{3}\right)V$
b. $v_C\left(t\right)=-40\cos \left(90t+\frac{\pi }{2}\right)V$
c. $v_C\left(t\right)=28\cos \left(15t+\frac{\pi }{8}\right)V$
d. $v_C\left(t\right)=45\cos \left(120t+\frac{\pi }{4}\right)V$