Question

Convert $40°20\text{'}$ into radian measure.

Answer 1

Convert $40°20\text{'}$ into radian measure:

We know that $1$ degree $=$ $60$ min or $1$° $=$ $60$′
$40°20\text{'}$ $=$ $40°$ $+$ $20\text{'}$
$=$$40°+\left(\frac{20°}{60°}\right)$
$=$$40°+{\left(\frac{1}{3}\right)}^{°}$

$=$$\frac{120°+1°}{3°}$
$=$$\frac{121°}{3°}$
Also,
Radian measure $=$ ${\left(\frac{\mathrm{\pi }}{180}\right)}^{°}$ $\times$ Degree measure
$=$${\left(\frac{\mathrm{\pi }}{180}\right)}^{°}$ $\times$$\frac{121°}{3°}$
$=$${\left(\frac{121}{540}\right)}^{°}\mathrm{\pi }$
Therefore, $40°20\text{'}$ is equal to ${\left(\frac{121}{540}\right)}^{°}\mathrm{\pi }$ radians.