Question

Radian measure of ${175}^{\circ }{45}^{\prime }$ is

• A. $\frac{700}{720}\pi$
• B. $\frac{703}{720}\pi$
• C. $\frac{705}{720}\pi$
• D. $\frac{710}{720}\pi$

Answer 1

Answer: (B)

$\frac{703}{720}\pi$

${175}^0{45}^{\prime }={(175+\frac{45}{60})}^0$
$={(175+\frac{3}{4})}^0$
$={\left(\frac{703}{4}\right)}^0$
Now, $1^0=\frac{\pi }{180}\text{radian}$
$\Rightarrow {\left(\frac{703}{4}\right)}^0=\frac{\pi }{180}\times \frac{703}{4}$
$=\frac{703}{720}\pi$
Option $B$ is correct.