Question

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

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