Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 1 - Trigonometric Functions - Section 1.3 Trigonometric Functions - 1.3 Exercises - Page 26: 56

Answer

$sin ~\theta = 0$ $cos ~\theta = -1$ $tan ~\theta = 0$ $csc ~\theta$ is undefined $sec ~\theta = -1$ $cot ~\theta$ is undefined

Work Step by Step

$y = 0, x \leq 0$ Since $x\leq 0$, we can let $x = -1$ and $y = 0$ Then $r = \sqrt{(-1)^2+(0)^2} = 1$ We can find the values of the six trigonometric functions: $sin ~\theta = \frac{y}{r} = \frac{0}{1} = 0$ $cos ~\theta = \frac{x}{r} = \frac{-1}{1} = -1$ $tan ~\theta = \frac{y}{x} = \frac{0}{-1} = 0$ $csc ~\theta = \frac{r}{y} = \frac{1}{0}$ (undefined) $sec ~\theta = \frac{r}{x} = \frac{1}{-1} = -1$ $cot ~\theta = \frac{x}{y} = \frac{-1}{0}$ (undefined)
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