Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 123: 12

Answer

(a) $0$ (b) $-1$ (c) $0$

Work Step by Step

You are given that $s=\pi$. (a) $\sin(s)=\sin(\pi)$ The angle $\pi$ intersects the unit circle at $(-1, 0)$, and since $sine$ gives the y-coordinate, the value of $\sin(\pi)$ is $0$. (b) $\cos(s)=\cos(\pi)$ The angle $\pi$ intersects the unit circle at $(-1, 0)$, and since $cosine$ gives the x-coordinate, the value of $\cos(\pi)$ is $-1$. (c) $\tan(s)=\tan(\pi)$ The angle $\pi$ intersects the unit circle at $(-1, 0)$, and since $tangent$ gives $\frac{y}{x}$, the value of $\tan(\pi)$ is $\frac{0}{-1}$, which simplifies to $0$.
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