Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.2 The Unit Circle and Circular Functions - 6.2 Exercises - Page 589: 57



Work Step by Step

RECALL: The quadrantal angles are: Positive x-axis: $0$ radians; Positive y-axis: $\frac{3.14}{2} = 1.57$ radians; Negative x-axis: $3.14$ radians; Negative y-axis: $4.61$ radians Positive x-axis: $6,18$ radians Thus, when moving counterclockwise from the positive x-axis, the angle $2$ radians is beyond the positive y-axis but before the negative x-axis. This means that the angle is in Quadrant II. With $\cos{\theta}=x$, and since the value of $x$ is negative in Quadrant II, then $\cos{2}$ must be negative.
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