Question

Express $50^{\circ }37^{\prime }30^{\prime \prime }$ in radian.

• A. $7\pi /32$
• B. $5\pi /32$
• C. $9\pi /32$
• D. $\pi /32$

Answer 1

Answer: (C)

Here, $30^{\prime \prime }={\left(\frac{30}{60}\right)}^{\prime }={\left(\frac{1}{2}\right)}^{\prime }$
Now, $37^{\prime }30^{\prime \prime }=37^{\prime }+{\left(\frac{1}{2}\right)}^{\prime }$
$={\left(\frac{75}{2}\right)}^{\prime }={\left(\frac{75}{2\times 60}\right)}^{\circ }={\left(\frac{5}{8}\right)}^{\circ }$
$\therefore 50^{\circ }37^{\prime }30^{\prime \prime }=50^{\circ }+{\left(\frac{5}{8}\right)}^{\circ }={\left(\frac{405}{8}\right)}^{\circ }$
Hence, ${\left(\frac{405}{8}\right)}^{\circ }=\frac{405}{8}\times \frac{\pi }{180}rad$
$=\frac{9\pi }{32}rad$