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: 51

Answer

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

Work Step by Step

Given $t=\frac{3\pi}{4}$, the terminal side is in quadrant II and $t_0=\frac{\pi}{4}$ to the $-x$-axis , we have: $sin(t)=sin(t_0)=\frac{\sqrt 2}{2}$, $cos(t)=-cos(t_0)=-\frac{\sqrt 2}{2}$, $tan(t)=-tan(t_0)=-1$, $cot(t)=-cot(t_0)=-1$, $sec(t)=-sec(t_0)=-\sqrt 2$, $csc(t)=csc(t_0)=\sqrt 2$.
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