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Chapter 4: Problem 44

Convert the angle measure from radians to degrees. Round to three decimal places. $$\frac{15 \pi}{8}$$

Short Answer

Expert verified
The converted angle measure from radians to degrees is approximately 337.500 degrees.

Step by step solution

01

Recognize the Conversion Formula

The formula to convert radians to degrees is as follows: \(degrees = radians \times \frac{180}{\pi}\). Here, \(\pi\) is roughly 3.14159265.
02

Substitute Radian Value

The next step is substituting the radian value into the formula. This gives: \(degrees = \frac{15 \pi}{8} \times \frac{180}{\pi}\). It's noted here that \(\pi\) in the numerator and \(\pi\) in the denominator will cancel out each other.
03

Simplify the Expression

Simplify the expression to: \(degrees = \frac{15 \times 180}{8}\).
04

Compute the Result

Multiply \(15\) by \(180\) and divide by \(8\) to get the degree measure.
05

Round to three decimal

Lastly, round to three decimal places as specified in the problem.

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