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: 55

Answer

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

Work Step by Step

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