Problem 18 - Precalculus: A Concise Course

Question

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(\frac{11 \pi}{8}\) (b) \(\frac{9 \pi}{8}\)

Step-by-Step Solution

Answer

Both \( \frac{11 \pi}{8} \) and \( \frac{9 \pi}{8} \) lie in Quadrant III.

Step 1: Analyze the First Angle

First, consider the angle \( \frac{11 \pi}{8} \). This angle is greater than \( \pi \) (180 degrees) and less than \( \frac{3\pi}{2} \) (270 degrees), which means it lies in Quadrant III.

Step 2: Analyze the Second Angle

Now, consider the angle \( \frac{9\pi}{8} \). This angle is also greater than \( \pi \) and less than \( \frac{3\pi}{2} \), so it too lies in Quadrant III.