Problem 22 - Precalculus Essentials

Question

Convert each angle in radians to degrees. $$\frac{\pi}{9}$$

Step-by-Step Solution

Answer

The angle \(\frac{\pi}{9}\) radians equals to 20 degrees.

Step 1: Understanding the Exercise

The exercise is to convert the angle \(\frac{\pi}{9}\) radians into degrees. The common conversion factor is \(180^\circ/\pi\) radians. This implies that \(\pi\) radians equals \(180^\circ\). It is important to understand what 'radian' and 'degree' are as units of angle. This conversion is necessary in various mathematical and physical computations.

Step 2: Conversion Process

To convert radians to degrees, multiply the radians by the conversion factor. This implies: \(\frac{\pi}{9}\) radians * \(180^\circ/\pi\) radians. Here the \(\pi\) gets cancelled out.

Step 3: Calculation

After cancelling the \(\pi\) out from the equation we get \(\frac{180}{9} = 20^\circ\)