Find the Radian Measure Corresponding to the Following Degree Measure : \( -47^\circ 30′ \)

First convert minutes into degrees:

\[ 30′ = \frac{30}{60}^\circ = \frac{1}{2}^\circ \]

Therefore,

\[ -47^\circ 30′ = -47.5^\circ = -\frac{95}{2}^\circ \]

To convert a degree measure into radians, we use the formula:

\[ \text{Radian} = \text{Degree} \times \frac{\pi}{180^\circ} \]

Conversion into Radians

\[ -\frac{95}{2}^\circ \times \frac{\pi}{180^\circ} \]

\[ = -\frac{95\pi}{360} \]

\[ = -\frac{19\pi}{72} \]

Answer

\[ -\frac{19\pi}{72} \]