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: 34

Answer

$\sin$(-855) = -$\frac{\sqrt2}{2}$ $\cos$(-855) = -$\frac{\sqrt2}{2}$ $\tan$(-855) = 1 $\cot$(-855) = 1 $\csc$(-855) = $-\sqrt2$ $\sec$(-855) = $-\sqrt2$

Work Step by Step

-855$^{\circ}$ We must first fine the coterminal angle: -855$^{\circ}$ + 360$^{\circ}$ = -495$^{\circ}$ -495$^{\circ}$ + 360$^{\circ}$ = -135$^{\circ}$ -135$^{\circ}$ + 360$^{\circ}$ = 255$^{\circ}$ 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}$ = 225$^{\circ}$ - 180$^{\circ}$ = 40$^{\circ}$ $\sin$(30) = -$\frac{1}{\sqrt2}$ = -$\frac{\sqrt2}{2}$ $\cos$(30) = -$\frac{1}{\sqrt2}$ = -$\frac{\sqrt2}{2}$ $\tan$(30) = $\frac{-1}{-1}$ = 1 $\cot$(30) = $\frac{-1}{-1}$ = 1 $\csc$(30) = -$\frac{\sqrt2}{1}$ = $-\sqrt2$ $\sec$(30) = -$\frac{\sqrt2}{1}$ = $-\sqrt2$
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