Answer
(a) $\frac{7\pi}{3}$
(b) $\frac{\pi}{12}$
(c) $\frac{5\pi}{4}$
(d) $\frac{11\pi}{12}$
Work Step by Step
Use the concept $1^\circ=\frac{\pi}{180}\,\text{rad}$ for all parts.
(a) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}420^\circ&=\left(\frac{\pi}{180}\cdot420\right)\,\text{rad}\\&=\frac{7\pi}{3}\,\text{rad}\end{aligned}$
So, the radian measure of given angle is $\frac{7\pi}{3}$.
(b) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}15^\circ&=\left(\frac{\pi}{180}\cdot15\right)\,\text{rad}\\&=\frac{\pi}{12}\,\text{rad}\end{aligned}$
So, the radian measure of given angle is $\frac{\pi}{12}$.
(c) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}225^\circ&=\left(\frac{\pi}{180}\cdot225\right)\,\text{rad}\\&=\frac{5\pi}{4}\,\text{rad}\end{aligned}$
So, the radian measure of given angle is $\frac{5\pi}{4}$.
(d) Multiply the given degree by conversion factor $\frac{\pi}{180}$.
$\begin{aligned}165^\circ&=\left(\frac{\pi}{180}\cdot165\right)\,\text{rad}\\&=\frac{11\pi}{12}\,\text{rad}\end{aligned}$
So, the radian measure of given angle is $\frac{11\pi}{12}$.
