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: 18

Answer

(a) $\sin{(-\frac{3\pi}{2})}=1$ (b) $\cos{(-\frac{3\pi}{2})}=0$ (c) $\tan{(-\frac{3\pi}{2})}=\dfrac{1}{0}, \text{ undefined}$

Work Step by Step

Using Figure 13 on page 579 of this book, the angle $-\frac{3\pi}{2}$, which is $\frac{3\pi}{2}$ units clockwise from the positive x-axis, intersects the unit circle at the point $(0, 1)$. RECALL: In a unit circle, (1) $\cos{s} = x$ (2) $\sin{s} = y$ (3) $\tan{s} = \dfrac{y}{x}$ Thus, use the definitions above to obtain: (a) $\sin{(-\frac{3\pi}{2})}=1$ (b) $\cos{(-\frac{3\pi}{2})}=0$ (c) $\tan{(-\frac{3\pi}{2})}=\dfrac{1}{0}, \text{ undefined}$
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