Problem 61 - Precalculus: A Concise Course

Question

Rewrite each angle in degree measure. (Do not use a calculator.) (a) \(\frac{3 \pi}{2}\) (b) \(\frac{7 \pi}{6}\)

Step-by-Step Solution

Answer

(a) \(\frac{3 \pi}{2}\) radians = \(270\) degrees. (b) \(\frac{7 \pi}{6}\) radians = \(210\) degrees.

Step 1: Understand the conversion factor

The conversion factor between radians and degrees is \(1 \, \text{radian} = \frac{180}{\pi} \, \text{degrees}\). This conversion factor will be used to convert the given radians to degrees.

Step 2: Convert \(\frac{3 \pi}{2}\) radians to degrees

Apply the conversion factor to \(\frac{3 \pi}{2}\) radians. Multiply \(\frac{3 \pi}{2}\) by \(\frac{180}{\pi}\) which gives \(270\) degrees.

Step 3: Convert \(\frac{7 \pi}{6}\) radians to degrees

Apply the conversion factor to \(\frac{7 \pi}{6}\) radians. Multiply \(\frac{7 \pi}{6}\) by \(\frac{180}{\pi}\) which gives \(210\) degrees.