For the $RL($high$-$pass$)$ filter shown below

a$)$ Derive the magnitude and phase angle of the transfer function in terms of $f,L$ and $R.$

For parts b$)-$d$)$ assume that $R=20$ and $L=10mH.$

b$)$ Plot the magnitude and phase of the transfer function versus the $lo{g}_{10}$ of the frequency in $(Hz)$

c$)$ Create a BODE plot and find the cutoff frequency for the filter

d$)$ Find $v_{\text{o}\text{u}\text{t}}$ if $v_{bn}=3+4cos(1000t)+5cos(2000t-30)$