Problem 37 - Precalculus Essentials

Question

Convert each angle in radians to degrees. Round to two decimal places. $$\frac{\pi}{13} \text { radians }$$

Step-by-Step Solution

Answer

So, \(\frac{\pi}{13}\) radians is approximately \(13.85^\circ\) degrees.

Step 1: Identifying the given value

The given angle is \(\frac{\pi}{13}\) radians.

Step 2: Using the conversion factor

The conversion factor from radians to degrees is \(\frac{180}{\pi}\). This is because \(\pi\) radians is equivalent to 180 degrees. Therefore, we multiply the given angle by this conversion factor.

Step 3: Calculation

To find the degree equivalent of \(\frac{\pi}{13}\) radians, multiply the given radian \(\frac{\pi}{13}\) by the conversion factor \(\frac{180}{\pi}\): \[\frac{\pi}{13} \cdot \frac{180}{\pi} = \frac{180}{13}\]

Step 4: Rounding the Result

The final step is to round the obtained result to the nearest two decimal places: \[\frac{180}{13} ≈ 13.85\]