Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.2 Trigonometric Functions: Unit Circle Approach - 6.2 Assess Your Understanding - Page 379: 81

Answer

$sin(\theta) =-\frac{\sqrt {2}}{2}$, $cos(\theta) =-\frac{\sqrt {2}}{2}$, $tan(\theta) =1$, $cot(\theta) =1$, $sec(\theta) =-\sqrt 2$, $csc(\theta) =-\sqrt 2$.

Work Step by Step

Given $x=-2,y=-2$, the terminal side is in quadrant III with $r=\sqrt {x^2+y^2}=2\sqrt {2}$, we have: $sin(\theta)=\frac{y}{r}=-\frac{\sqrt {2}}{2}$, $cos(\theta)=\frac{x}{r}=-\frac{\sqrt {2}}{2}$, $tan(\theta)=\frac{y}{x}=1$, $cot(\theta)=\frac{x}{y}=1$, $sec(\theta)=\frac{r}{x}=-\sqrt 2$, $csc(\theta)=\frac{r}{y}=-\sqrt 2$.
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