Precalculus (10th Edition)

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

Chapter 8 - Applications of Trigonometric Functions - 8.1 Right Triangle Trigonometry; Applications - 8.1 Assess Your Understanding - Page 519: 9


$\sin\theta=\dfrac{5}{13}$ $\cos\theta=\dfrac{12}{13}$ $\tan\theta=\dfrac{5}{12}$ $\cot\theta=\dfrac{12}{5}$ $\sec\theta=\dfrac{13}{12}$ $\csc\theta=\dfrac{13}{5}$

Work Step by Step

Let's note: $h$=the hypotenuse $o$=the opposite side of angle $\theta$ $a$=the adjacent side of angle $\theta$ We are given: $o=5$ $a=12$ Determine the hypotenuse, using the Pythagorean Theorem: $h^2=o^2+a^2$ $h^2=5^2+12$ $h^2=169$ $h=\pm\sqrt{169}$ $h=\pm13$ Since $h$ is never negative, then $h=13$. Determine the $6$ trigonometric functions of angle $\theta$: $\sin\theta=\dfrac{o}{h}=\dfrac{5}{13}$ $\cos\theta=\dfrac{a}{h}=\dfrac{12}{13}$ $\tan\theta=\dfrac{o}{a}=\dfrac{5}{12}$ $\cot\theta=\dfrac{a}{o}=\dfrac{12}{5}$ $\sec\theta=\dfrac{h}{a}=\dfrac{13}{12}$ $\csc\theta=\dfrac{h}{o}=\dfrac{13}{5}$
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