Question

The radian measure of $175°45\text{'}$ is

Answer 1

Finding the radian measure of the given angle:

The given expression is $175°45\text{'}$

$175°45\text{'}$$={\left(175+\frac{45}{60}\right)}^{°}$

$={\left(175+\frac{3}{4}\right)}^{°}$

$={\left(\frac{175\times 4+3}{4}\right)}^{°}$

$={\left(\frac{703}{4}\right)}^{°}$

We know that $1°=\frac{\mathrm{\pi }}{180}radian$

${\left(\frac{703}{4}\right)}^{°}=\frac{\mathrm{\pi }}{180}\times \frac{703}{4}$

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

Hence, the radian measure of $175°45\text{'}$ is $\frac{703}{720}\mathrm{\pi }$.