Problem 60 - Precalculus: A Concise Course

Question

Rewrite each angle in radian measure as a multiple of \(\pi\). (Do not use a calculator.) (a) \(-270^{\circ}\) (b) \(144^{\circ}\)

Step-by-Step Solution

Answer

(a) \( -\frac{3 \pi}{2} \) \n(b) \( \frac{4 \pi}{5} \)

Step 1: Convert -270 degrees into radians

For part (a), use the conversion formula by plugging -270 into the place of degrees: \( \text{radians} = -270 \times \frac{\pi}{180} \) . This can be simplified to \( -\frac{3 \pi}{2} \).

Step 2: Convert 144 degrees into radians

For part (b), again use the conversion formula, this time plugging 144 into the place of degrees: \( \text{radians} = 144 \times \frac{\pi}{180} \). This can be simplified to \( \frac{4 \pi}{5} \).