Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.1 - The Unit Circle - 5.1 Exercises - Page 408: 48

Answer

(a) Reference Number: $\pi/6$ (b) Terminal point: $(\sqrt 3/2, 1/2)$

Work Step by Step

1. $13\pi/6 \gt 2\pi$. Subtract $2\pi$ from it until the result is less than $2\pi$. $$\frac{13\pi}{6} - 2\pi = \frac{13\pi}{6} -\frac{12\pi}{6} = \frac{\pi}{6}$$ 2. $\pi/6$ is in Quadrant I, thus, the Reference Number is $\pi/6$: $$t^- = \frac{\pi}{6}$$ 3. According to the Table 1, the terminal point for $\pi/6$ is $(\sqrt 3/2, 1/2)$. Since the terminal point must be in Quadrant I, the x-coordinate is positive, and the y-coordinate is also positive. Therefore, the terminal point for $t = 13\pi/6$ is $(\sqrt 3/2, 1/2)$
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