Trigonometry (10th Edition)

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

Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 118: 53

Answer

$\sin\theta =-\displaystyle \frac{12}{13}$ $\cos\theta =\displaystyle \frac{5}{13}$ $\tan\theta =-\displaystyle \frac{12}{5}$ $\cot\theta =-\displaystyle \frac{5}{12}$ $\sec\theta =\displaystyle \frac{13}{5}$ $\csc\theta =-\displaystyle \frac{13}{12}$

Work Step by Step

For any real number $s$ represented by a directed arc on the unit circle, $\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$ $\displaystyle \csc s=\frac{1}{y} (y\neq 0)\quad \displaystyle \sec s=\frac{1}{x} (x\neq 0) \displaystyle \quad\cot s=\frac{x}{y} (y\neq 0)$. ------------------- $\displaystyle \sin\theta=y=-\frac{12}{13}$ $\displaystyle \cos\theta=x=\frac{5}{13}$ $\displaystyle \tan\theta=\frac{y}{x}=\frac{-\frac{12}{13}}{\frac{5}{13}}=-\frac{12}{13}(\frac{13}{5})=-\frac{12}{5}$ $\displaystyle \cot\theta=\frac{x}{y}=\frac{\frac{5}{13}}{-\frac{12}{13}}=\frac{5}{13}(-\frac{13}{12})=-\frac{5}{12}$ $\displaystyle \sec\theta=\frac{1}{x}=\frac{1}{\frac{5}{13}}=\frac{13}{5}$ $\displaystyle \csc\theta=\frac{1}{y}=\frac{1}{-\frac{12}{13}}=-\frac{13}{12}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.