Degree–radian conversion (II)

Statement

Convert from degrees to radians, or from radians to degrees:

• (a) $123^\circ$
• (b) $-1143^\circ$
• (c) $344\ \text{rad}$
• (d) $1{.}32\ \text{rad}$

Solution

Use $\alpha_{\text{rad}}=\dfrac{\pi}{180}\,\alpha_{\text{deg}}$ and $\alpha_{\text{deg}}=\dfrac{180}{\pi}\,\alpha_{\text{rad}}$.

• (a) $123^\circ=\dfrac{123\pi}{180}\approx2{.}1468\ \text{rad}$.
• (b) $-1143^\circ=-\dfrac{1143\pi}{180}\approx-19{.}949\ \text{rad}$ (reduced, $\equiv297^\circ\approx5{.}184\ \text{rad}$).
• (c) $344\ \text{rad}=344\cdot\dfrac{180}{\pi}\approx19709{.}7^\circ$ (reduced, $\approx269{.}9^\circ$).
• (d) $1{.}32\ \text{rad}=1{.}32\cdot\dfrac{180}{\pi}\approx75{.}63^\circ$.

$\boxed{2{.}1468\ \text{rad};\ -19{.}949\ \text{rad};\ 19709{.}7^\circ;\ 75{.}63^\circ}$