Chapter 6 - The Circular Functions and Their Graphs - 6.2 The Unit Circle and Circular Functions - 6.2 Exercises - Page 589: 59

negative

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 $5$ radians is beyond the negative y-axis but before the positive x-axis. This means that the angle is in Quadrant IV. With $\sin{\theta}=y$, and since the value of $y$ is negative in Quadrant IV, then $\sin{5}$ must be negative.

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