Converting Radians to Degrees

Because we are given radians and we want degrees, we should set up a proportion and solve it.

1. ⓐ We use the proportion, substituting the given information.
   $$\begin{array}{ccc}\hfill \frac{\theta }{180}& =& \frac{{\theta }_R}{\pi }\hfill \\ \hfill \frac{\theta }{180}& =& \frac{\frac{\pi }{6}}{\pi }\hfill \\ \hfill \theta & =& \frac{180}{6}\hfill \\ \hfill \theta & =& \mathrm{30°}\hfill \end{array}$$
2. ⓑ We use the proportion, substituting the given information.
   $$\begin{array}{ccc}\hfill \frac{\theta }{180}& =& \frac{{\theta }_{{}^R}}{\pi }\hfill \\ \hfill \frac{\theta }{180}& =& \frac{3}{\pi }\hfill \\ \hfill \theta & =& \frac{3(180)}{\pi }\hfill \\ \hfill \theta & \approx & \mathrm{172°}\hfill \end{array}$$