Problem 16 - Precalculus Essentials

Question

Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$150^{\circ}$$

Step-by-Step Solution

Answer

After converting \(150^{\circ}\) to radians, the result is \((5 \pi) / 6 \: rad\).

Step 1: Analysis and Approach

Given an angle in degrees and the task is to convert it into radians. The relationship between radians and degrees is as follows: \(180^{\circ} = \pi \: rad\). Thus to convert degrees to radians, the given degree value can be multiplied by \(\pi\) and divided by 180.

Step 2: Conversion

Given angle is \(150^{\circ}\). By applying the conversion formula, it will be \((150 \times \pi) / 180\).

Step 3: Simplification

After simplifying, one can observe that 150 and 180 have a common factor of 30, so after simplification, calculated radian value becomes \((5 \times \pi) / 6\).