Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.3 Properties of the Trigonometric Functions - 5.3 Assess Your Understanding - Page 418: 29


$\text{Quadrant IV}$

Work Step by Step

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