Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 5 - Trigonometric Functions - 5.3 Trigonometric Functions Values and Angle Measures - 5.3 Exercises - Page 531: 7

Answer

$negative$, $III$, $60^\circ$, $-\frac{\sqrt 3}{2}$.

Work Step by Step

We can identify $\theta=240^\circ$ to be in quadrant $III$, thus $sin\theta$ will be $negative$. The reference angle is the acute angle formed by its terminal line with x-axis and it can be found as $240^\circ-180^\circ=60^\circ$, thus the exact value is $sin240^\circ=-sin60^\circ=-\frac{\sqrt 3}{2}$. The answers are $negative$, $III$, $60^\circ$, $-\frac{\sqrt 3}{2}$.
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