Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises: 31

Answer

$\sin$(-510) = -$\frac{1}{2}$ $\cos$(-510) = -$\frac{\sqrt3}{2}$ $\tan$(-510) = $\frac{\sqrt3}{3}$ $\cot$(-510) = $\sqrt3$ $\csc$(-510) = -2 $\sec$(-510) = -$\frac{2\sqrt3}{3}$

Work Step by Step

-510$^{\circ}$ We must first fine the coterminal angle: -510$^{\circ}$ + 360$^{\circ}$ = -150$^{\circ}$ -150 is in Quadrant III. Therefore all the trigonometric functions are negative with the exception of $\tan$ and $\cot$ The reference angle is: $\theta$$^{1}$ = -150$^{\circ}$ +`180$^{\circ}$ = 30$^{\circ}$ $\sin$(30) = -$\frac{1}{2}$ $\cos$(30) = -$\frac{\sqrt3}{2}$ $\tan$(30) = $\frac{\sqrt3}{3}$ $\cot$(30) = $\sqrt3$ $\csc$(30) = -2 $\sec$(30) = -$\frac{2\sqrt3}{3}$
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