Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.3 - Definition I: Trigonometric Functions - 1.3 Problem Set - Page 31: 14

Answer

$\sin\theta$ = 0 $\cos\theta$ = -1 $\tan\theta$ = 0 $\cot\theta$ = Undefined $\sec\theta$ = -1 $\csc\theta$ = Undefined

Work Step by Step

Given, point (-3, 0) is on the terminal side of $\theta$, we may apply Definition I to find all six trigonometric functions- We got $ x = -3, y = 0$ Therefore r= $\sqrt (x^{2} + y^{2})$ = $\sqrt ((-3)^{2} + (0)^{2})$ = $\sqrt (9 + 0)$ = $\sqrt (9)$ = 3 i.e. $ x = -3, y = 0,$ and $ r= 3$ Applying Definition I- $\sin\theta$ =$ \frac{y}{r}$ = $ \frac{0}{3}$ = 0 $\cos\theta$ =$ \frac{x}{r}$ =$ \frac{-3}{3}$ = -1 $\tan\theta$ =$ \frac{y}{x}$ =$ \frac{0}{-3}$ = 0 $\cot\theta$ =$ \frac{x}{y}$ =$ \frac{-3}{0}$ = Undefined $\sec\theta$ =$ \frac{r}{x}$ =$ \frac{3}{-3}$ = -1 $\csc\theta$ =$ \frac{r}{y}$ =$ \frac{3}{0}$ = Undefined
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