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: 24



Work Step by Step

RECALL: $\sin{s} = y \\\cos{s} = x \\\tan{s} = \frac{y}{x} \\\cot{s} = \frac{x}{y} \\\sec{s} = \frac{1}{x} \\\csc{s}=\frac{1}{y}$ (refer to Figure 11 on page 111 of the textbook) A negative angle measure means the terminal side of the angle will move clockwise from the positive x-axis. Thus, from the positive x-axis, moving the terminal side $\frac{17\pi}{3}$ radians clockwise ends at $\frac{\pi}{3}$ in Figure 11. The angle $\frac{\pi}{3}$ intersects the unit circle at the point $(\frac{1}{2}, \frac{\sqrt3}{2})$. This point has: $x= \frac{1}{2}$ $y=\frac{\sqrt3}{2}$ Thus, $\tan{(-\frac{17\pi}{3}} \\= \tan{\frac{5\pi}{3}} \\=\dfrac{y}{x} \\=\dfrac{\frac{\sqrt3}{2}}{\frac{1}{2}} \\=\frac{\sqrt3}{2} \cdot \frac{2}{1} \\=\sqrt3$
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