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Chapter 4: Problem 64

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

Short Answer

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

Step by step solution

01

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 \(\frac{180}{\pi}\).
02

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.
03

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.

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