Precalculus (10th Edition)

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

Chapter 6 - Trigonometric Functions - 6.2 Trigonometric Functions: Unit Circle Approach - 6.2 Assess Your Understanding - Page 379: 54

Answer

$sin(t) =\frac{1}{2}$, $cos(t) =\frac{\sqrt 3}{2}$, $tan(t) =\frac{\sqrt 3}{3}$, $cot(t) =\sqrt 3$, $sec(t) =\frac{2\sqrt 3}{3}$, $csc(t) =2$.

Work Step by Step

Given $t=\frac{13\pi}{6}=2\pi+\frac{\pi}{6}$, the terminal side is in quadrant I and $t_0=\frac{\pi}{6}$ to the $+x$-axis , we have: $sin(t)=sin(t_0)=\frac{1}{2}$, $cos(t)=cos(t_0)=\frac{\sqrt 3}{2}$, $tan(t)=tan(t_0)=\frac{\sqrt 3}{3}$, $cot(t)=cot(t_0)=\sqrt 3$, $sec(t)=sec(t_0)=\frac{2\sqrt 3}{3}$, $csc(t)=csc(t_0)=2$.
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