Problem 64 - Precalculus: A Concise Course

Question

Rewrite each angle in degree measure. (Do not use a calculator.) (a) \(\frac{11 \pi}{6}\) (b) \(\frac{34 \pi}{15}\)

Step-by-Step Solution

Answer

The angle measures \(\frac{11 \pi}{6}\) radians and \(\frac{34 \pi}{15}\) radians are equivalent to 330 degrees and 408 degrees, respectively.

Step 1: Determine the Conversion Factor

In order to convert radians to degrees, the key factor to remember is that \(\pi\) radians is equivalent to \(180\) degrees. So, the conversion factor is \(\frac{180}{\pi}\).

Step 2: Convert 11pi/6 to Degrees

To convert \(\frac{11 \pi}{6}\) radians to degrees, multiply by the conversion factor \(\frac{180}{\pi}\). This cancels out \(\pi\) and switches the measurement to degrees: \( \frac{11 \pi}{6} \times \frac{180}{\pi} = 330 \) degrees.

Step 3: Convert 34pi/15 to Degrees

Similarly, to convert \(\frac{34 \pi}{15}\) radians to degrees, multiply by the conversion factor \(\frac{180}{\pi}\): \( \frac{34 \pi}{15} \times \frac{180}{\pi} = 408 \) degrees. Make sure to simplify properly and round as needed.