Problem 38 - Precalculus Essentials

Question

Convert each angle in radians to degrees. Round to two decimal places. $$\frac{\pi}{17} \text { radians }$$

Step-by-Step Solution

Answer

The value of \(\frac{\pi}{17}\) radians in degrees, rounded to two decimal places, is approximately 10.59 degrees.

Step 1: Know the Conversion Factor

Remember that the conversion factor between radians and degrees is that there are 180 degrees in \(\pi\) radians, or, equivalently, \(\frac{180}{\pi}\) degrees in 1 radian.

Step 2: Apply the Conversion Factor

To convert the given angle from radians to degrees, multiply the radian measure by the conversion factor. This results in an expression \(\frac{\pi}{17} \cdot \frac{180}{\pi}\). Notice how the \(\pi\) in the numerator and denominator will cancel each other.

Step 3: Perform the Calculation

Finally, calculate the resulting expression. This will give a numerical value for the degree measure which should be rounded to two decimal places as instructed by the problem.