Question

The radian measure of $-{37}^{\circ }{30}^{\prime }$ is

• A. $-\frac{5\pi }{24}$
• B. $-\frac{\pi }{8}$
• C. $-\frac{3\pi }{8}$
• D. $-\frac{7\pi }{24}$

Answer 1

The correct option is A $-\frac{5\pi }{24}$

We know that,
${60}^{\prime }=1^{\circ }\Rightarrow {30}^{\prime }={\frac{1}{2}}^{\circ }$
Now, $-{37}^{\circ }{30}^{\prime }=-({37}^{\circ }+{\frac{1}{2}}^{\circ })=-{\frac{75}{2}}^{\circ }$
Converting it into radian, we get
$-{37}^{\circ }{30}^{\prime }=-{\frac{75}{2}}^{\circ }\times \frac{\pi }{{180}^{\circ }}=-\frac{5\pi }{24}$