Question

Find the degree measure corresponding to the following radian measure: 
(−3)^c

Answer 1

We have: 
\[\pi \text{ rad }= 180^\circ\]
\[ \therefore 1 \text{ rad }= \left( \frac{180}{\pi} \right)^\circ \]
\[\left( - 3 \right)^c = \left( \frac{180}{\pi} \times - 3 \right)^\circ \]
\[ = \left( \frac{180}{22} \times 7 \times - 3 \right)^\circ\]
\[ = \left( \frac{- 3780}{22} \right)^\circ\]
\[ = \left( - 171\frac{18}{22} \right)^\circ\]
\[ = \left\{ - 171^\circ \left( \frac{18}{22} \times 60 \right)^′  \right\}\]
\[ = \left\{ - 171^\circ \left( 49\frac{1}{11} \right)^′ \right\}\]
\[ = - \left\{ 171^\circ 49' \left( \frac{1}{11} \times 60 \right)^{''} \right\}\]
\[ = - \left( 171^\circ 49' 5. {45}^{''} \right) \]
\[ \approx - \left( 171^\circ 49' 5^{''} \right)\]