Question

Find the radian measure corresponding to the following degree measure: 125° 30'

Answer 1

We have:
\[180^\circ = \pi \text{ rad }\]
\[ \therefore 1^\circ = \frac{\pi}{180} \text{ rad }\]
\[ 30' = \left( \frac{1}{2} \right)^\circ \]
\[ \therefore 125^\circ  30' = \left( 125\frac{1}{2} \right)^\circ \]
\[ = \left( \frac{251}{2} \right)^\circ \]
\[ = \frac{251}{2} \times \frac{\pi}{180}\]
\[ = \frac{251\pi}{360} \text{ rad }\]