Problem 41 - Precalculus: A Concise Course

Question

Determine the quadrant in which each angle lies. (a) \(130^{\circ}\) (b) \(285^{\circ}\)

Step-by-Step Solution

Answer

Angle \(130^{\circ}\) is in Quadrant II and angle \(285^{\circ}\) is in Quadrant IV.

Step 1: Check the first angle

Given the angle is \(130^{\circ}\). Comparing it with the range of angles in each quadrant, it can be seen that this angle lies within the angle range for Quadrant II (from \(90^{\circ}\) to \(180^{\circ}\)). As a result, \(130^{\circ}\) lies in Quadrant II.

Step 2: Check the second angle

Given the angle is \(285^{\circ}\). Comparing it with the range of angles in each quadrant, it can be seen that this angle lies within the angle range for Quadrant IV (from \(270^{\circ}\) to \(360^{\circ}\)). As a result, \(285^{\circ}\) lies in Quadrant IV.