Question

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

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

Answer 1

Answer: (C)

Here, $30''=\left(\frac{30}{60}\right)'=\left(\frac{1}{2}\right)'$
Now, $37'\,30''=37'+\left(\frac{1}{2}\right)'$
$=\left(\frac{75}{2}\right)'=\left(\frac{75}{2\times60}\right)^{\circ}=\left(\frac{5}{8}\right)^{\circ}$
$\therefore 50^{\circ}37'30''=50^{\circ}+\left(\frac{5}{8}\right)^{\circ}=\left(\frac{405}{8}\right)^{\circ}$
Hence, $\left(\frac{405}{8}\right)^{\circ}=\frac{405}{8}\times\frac{\pi}{180} rad$
$=\frac{9\pi}{32} rad$