Question

Find the circular measure of the following angle $-22^{\circ}30'$

• A. $- \frac{\pi}{8}$
• B. $\frac{\pi}{12}$
• C. $- \frac{\pi}{12}$
• D. $\frac{\pi}{4}$

Answer 1

Answer: (A)

Since $180^{\circ}=\pi$ radian, therefore,
$1^{\circ}=\frac{\pi}{180}$ radian
$\Rightarrow \left(-22^{\circ}30'\right)=\left(-22 \frac{1}{2}\right)^{\circ}$
$=\frac{\pi}{180}\left(-\frac{45}{2}\right)$ radian
$=-\frac{\pi}{8}$ radian $\,\left(\because 30'=\left(\frac{30}{60}\right)^{\circ}=\left(\frac{1}{2}\right)^{\circ}\right)$