Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.2 - Radians and Degrees - 3.2 Problem Set - Page 133: 57



Work Step by Step

$\dfrac{4\pi}{3}$ is an angle in Quadrant III. The reference angle of an angle in Quadrant III can be found using the formula $\theta - \pi$. Thus, the reference angle of $\dfrac{4\pi}{3}$ is: $\dfrac{4\pi}{3} - \pi = \dfrac{4\pi}{3}-\dfrac{3\pi}{3} = \dfrac{\pi}{3}$ $\dfrac{\pi}{3}$ is a special angle whose sine value is $\dfrac{\sqrt3}{2}$. However, since $\dfrac{4\pi}{3}$ is in Quadrant III, then its sine value is negative. Thus, $\sin{(\frac{4\pi}{3})}=-\frac{\sqrt3}{2}$
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