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: 77

Answer

$sin(\theta) =\frac{4}{5}$, $cos(\theta) =-\frac{3}{5}$, $tan(\theta) =-\frac{4}{3}$, $cot(\theta) =-\frac{3}{4}$, $sec(\theta) =-\frac{5}{3}$, $csc(\theta) =\frac{5}{4}$.

Work Step by Step

Given $x=-3,y=4$, the terminal side is in quadrant II with $r=\sqrt {x^2+y^2}=5$, we have: $sin(\theta)=\frac{y}{r}=\frac{4}{5}$, $cos(\theta)=\frac{x}{r}=-\frac{3}{5}$, $tan(\theta)=\frac{y}{x}=-\frac{4}{3}$, $cot(\theta)=\frac{x}{y}=-\frac{3}{4}$, $sec(\theta)=\frac{r}{x}=-\frac{5}{3}$, $csc(\theta)=\frac{r}{y}=\frac{5}{4}$.
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