Problem 14 - Precalculus Essentials

Question

Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$18^{\circ}$$

Step-by-Step Solution

Answer

So, \(18^{\circ}\) is equal to \(\frac{\pi}{10}\) radians.

Step 1: Identify the given angle

The angle given in the problem is \(18^{\circ}\).

Step 2: Use the conversion factor

We know the conversion factor between degrees and radians, which is \(\frac{\pi}{180^{\circ}}\). Multiply the given angle by this conversion factor to convert it into radians.

Step 3: Perform the multiplication

Multiply the given angle \(18^{\circ}\) by the conversion factor from Step 2, which results in \((18 * \frac{\pi}{180})\) radians.

Step 4: Simplify the result

Simplify the resulting expression. \(18 * \frac{\pi}{180}\) simplifies to \(\frac{\pi}{10}\).