Problem 58 - Precalculus: A Concise Course

Question

Rewrite each angle in radian measure as a multiple of \(\pi\). (Do not use a calculator.) (a) \(315^{\circ}\) (b) \(120^{\circ}\)

Step-by-Step Solution

Answer

In radian measures, \(315^{\circ} = \frac{7\pi}{4}\) and \(120^{\circ} = \frac{2\pi}{3}\)

Step 1: Convert 315 degrees to radians

To convert an angle from degrees to radians, we use the formula \(\text{radians} = \frac{\pi}{180} \times \text{angle in degrees}\). Applying this formula to the given angle \(\text{radians (for 315 degrees)} = \frac{\pi}{180} \times 315 = \frac{7\pi}{4}\).

Step 2: Convert 120 degrees to radians

Using the same formula as above for conversion, we find that \(\text{radians (for 120 degrees)} = \frac{\pi}{180} \times 120 = \frac{2\pi}{3}\).