Question

complete each statement in exercises 39 - 42, where $\theta$ is the measure of $angle aob$ in standard position. assume that $\theta$ is in the given interval. 39. $0^{circ}<\theta<90^{circ}$; $angle aob$ lies in quadrant ?. 40. $180^{circ}<\theta<270^{circ}$; $angle aob$ lies in quadrant ?. 41. $90^{circ}<\theta<180^{circ}$; $angle aob$ lies in quadrant ?. 42. $-90^{circ}<\theta<0^{circ}$; $angle aob$ lies in quadrant ?.

Explanation:

Step1: Recall quadrant - angle relationships

Angles between \(0^{\circ}\) and \(90^{\circ}\) are in the first quadrant.

Step2: Analyze second - interval

Angles between \(180^{\circ}\) and \(270^{\circ}\) are in the third quadrant.

Step3: Analyze third - interval

Angles between \(90^{\circ}\) and \(180^{\circ}\) are in the second quadrant.

Step4: Analyze fourth - interval

Angles between \(- 90^{\circ}\) and \(0^{\circ}\) are in the fourth quadrant.

Answer:

1. First
2. Third
3. Second
4. Fourth