Answer
(a) $\frac{5\pi}{12}$
(b) $\frac{13\pi}{6}$
(c) $\frac{\pi}{9}$
(d) $\frac{23\pi}{30}$
Work Step by Step
Use the concept $1^{\text o}=\frac{\pi}{180}\, \text {rad}$ for all parts.
(a) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}75^{\text o}&=\left(\frac{\pi}{180}\cdot75\right)\, \text {rad}
\\&=\frac{5\pi}{12}\,\text{rad}\end {aligned}$
So, the radian measure of given angle is $\frac{5\pi}{12}$.
(b) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}390^{\text o}&=\left(\frac{\pi}{180}\cdot390\right)\, \text {rad}
\\&=\frac{13\pi}{6}\,\text{rad}\end {aligned}$
So, the radian measure of given angle is $\frac{13\pi}{6}$.
(c) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}20^{\text o}&=\left(\frac{\pi}{180}\cdot20\right)\, \text {rad}
\\&=\frac{\pi}{9}\,\text{rad}\end {aligned}$
So, the radian measure of given angle is $\frac{\pi}{9}$.
(d) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}138^{\text o}&=\left(\frac{\pi}{180}\cdot138\right)\, \text {rad}
\\&=\frac{23\pi}{30}\,\text{rad}\end {aligned}$
So, the radian measure of given angle is $\frac{23\pi}{30}$.
