Question

Find the radian measure corresponding to the following degree measure: 7° 30'

Answer 1

We have:
\[180^\circ = \pi \text{ rad }\]
\[ \therefore 1^\circ = \frac{\pi}{180} \text{ rad }\]
\[ 30' = \left( \frac{1}{2} \right)^\circ \]
\[ \therefore 7^\circ 30' = \left( 7\frac{1}{2} \right)^\circ \]
\[ = \left( \frac{15}{2} \right)^\circ \]
\[ = \frac{15}{2} \times \frac{\pi}{180}\]
\[ = \frac{\pi}{24}\text{ rad }\]