Problem 17 - Precalculus Essentials

Question

Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$300^{\circ}$$

Step-by-Step Solution

Answer

The angle of \(300^{\circ}\) is equal to \(5\pi/3\) radians.

Step 1: Identify the conversion factor from degrees to radians

The conversion factor from degrees to radians is \(\pi / 180^{\circ}\). This is because in the unit circle, an entire rotation is \(360^{\circ}\) or \(2\pi\) radians. Therefore, half of the rotation, \(180^{\circ}\) is equivalent to \(\pi\) radians.

Step 2: Convert the given angle from degrees to radians

To convert the given angle \(300^{\circ}\) to radians, multiply \(300^{\circ}\) by the conversion factor \(\pi / 180^{\circ}\). Thus, the calculation is as follows: \(300 \times (\pi / 180^{\circ}) = 5\pi/3\).