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 533: 75

Answer

$\frac{\sqrt 3}{2}$, $-\frac{1}{2}$, $ -\sqrt 3$, $ -\frac{\sqrt 3}{3}$, $ -2$, and $ \frac{2\sqrt 3}{3}$.

Work Step by Step

Given $\theta=480^\circ=360^\circ+120^\circ$ (quadrant II), we have $sin\theta =sin60^\circ=\frac{\sqrt 3}{2}$, $cos\theta =-cos60^\circ=-\frac{1}{2}$, $tan\theta =-tan60^\circ=-\sqrt 3$, $cot\theta = \frac{1}{tan\theta}=-\frac{\sqrt 3}{3}$, $sec\theta = \frac{1}{cos\theta}=-2$, and $csc\theta = \frac{1}{sin\theta}=\frac{2\sqrt 3}{3}$.
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