Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Test - Page 250: 9c


$tan(2\theta) = \frac{24}{7}$

Work Step by Step

If $90^{\circ} \lt \theta \lt 180^{\circ}$, then the angle $\theta$ is in quadrant II. If the hypotenuse is 5, and the adjacent side has a length of 3, then the length of the opposite side is $\sqrt{5^2-3^2} = 4$ From part (a), we know that $cos(2\theta) = -\frac{7}{25}$ From part (b), we know that $sin(2\theta) = -\frac{24}{25}$ We can find $tan(2\theta)$: $tan(2\theta) = \frac{sin(2\theta)}{cos(2\theta)}$ $tan(2\theta) = \frac{-\frac{24}{25}}{-\frac{7}{25}}$ $tan(2\theta) = \frac{24}{7}$
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