Problem 62 - Precalculus: A Concise Course

Question

Rewrite each angle in degree measure. (Do not use a calculator.) (a) \(-\frac{7 \pi}{12}\) (b) \(\frac{\pi}{9}\)

Step-by-Step Solution

Answer

The angle \(-\frac{7 \pi}{12}\) radians is equal to -105 degrees and the angle \(\frac{\pi}{9}\) radians is equal to 20 degrees.

Step 1: Convert the first angle from radians to degrees

The first angle given is \(-\frac{7 \pi}{12}\) radians. To convert this to degrees, multiply by the factor \(\frac{180}{\pi}\) degrees/radian. The \(\pi\) in the numerator of the angle and the \(\pi\) in the denominator of the conversion factor will cancel out. So the calculation becomes: \(-\frac{7 \pi}{12} \times \frac{180}{\pi} = -\frac{7 \times 180}{12} = -105\). Therefore, \(-\frac{7 \pi}{12}\) radians is exactly -105 degrees.

Step 2: Convert the second angle from radians to degrees

The second angle given is \(\frac{\pi}{9}\) radians. Similar to the first angle, to convert this to degrees, multiply by the conversion factor \(\frac{180}{\pi}\). Thus, we get \(\frac{\pi}{9} \times \frac{180}{\pi}\). The \(\pi\) in the numerator of the angle and the \(\pi\) in the denominator of the conversion factor will cancel out, leaving: \(\frac{1 \times 180}{9} = 20\). Therefore, \(\frac{\pi}{9}\) radians is exactly 20 degrees.