# Chapter 5 - Trigonometric Functions - Section 5.3 Properties of the Trigonometric Functions - 5.3 Assess Your Understanding - Page 418: 32

$\text{Quadrant III}$

#### Work Step by Step

$P= (x,y) \text{ is the point on the unit circle corresponding to } \theta$ We have: $\cos{\theta} = x<0$ $\tan{\theta} = \dfrac{y}{x} >0$ With $x<0 \text{ and } \text{\theta} \gt 0$, then $y\lt 0$ Note that points in Quadrant III have $y\lt 0 \text{ and } x<0$ Thus, $\theta \in \text{Quadrant III}$.

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