Chapter 6.3, Problem 34AYU

To determine

To find: The quadrant in which the angle $\theta$ lies.

Answer to Problem 34AYU

Solution:

Quadrant II.

Explanation of Solution

Given:

$\text{csc}\theta >0,\text{cos}\theta <0$

Calculation:

Let $P = \left(x, y\right)$ be the point on the unit circle corresponding to $\theta$. Then $\text{csc}\theta =\frac{1}{y}>0$ and $\text{cos}\theta =x<0$. Because points in quadrant II have $x<0$ and $y>0$, $\theta$ lies in quadrant II.