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Chapter 4: Problem 45

Convert the angle measure from radians to degrees. Round to three decimal places. $$-4.2 \pi$$

Short Answer

Expert verified
-756.000 degrees

Step by step solution

01

Understand the conversion formula.

The formula to convert radians to degrees is given by \(angle_{degrees} = angle_{radians} \times \frac{180}{\pi}\). This equation works because the ratio between a circle鈥檚 circumference and its diameter is \(2 \pi\) in radian terms and 360 in degree terms.
02

Apply the formula to the given value.

Now, use the formula to convert the given angle -4.2 pi radians into degrees. Substitute into the formula as follows: \(-4.2 \pi \times \frac{180}{\pi}\).
03

Simplify and round to three decimal places.

The \(\pi\) factors will cancel out, largely simplifying the problem. Next, carry out the remaining multiplication and round the answer to three decimal places.

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