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: 36

Answer

$\sin$(45) = $\frac{-\sqrt2}{2}$ $\cos$(45) = $\frac{\sqrt2}{2}$ $\tan$(45) = -1 $\cot$(45) = -1 $\csc$(45) = -$\sqrt2$ $\sec$(45) = $\sqrt2$

Work Step by Step

-2205$^{\circ}$ We must first fine the coterminal angle: -2205$^{\circ}$ + 7(360$^{\circ}$) = 315$^{\circ}$ 315 is in Quadrant IV. Therefore all the trigonometric functions are negative with the exception of $\cos$ and $\sec$. The reference angle is: $\theta$$^{1}$ = 360$^{\circ}$ - 315$^{\circ}$ = 45$^{\circ}$ $\sin$(45) = $\frac{-1}{\sqrt2}$ = $\frac{-\sqrt2}{2}$ $\cos$(45) = $\frac{1}{\sqrt2}$ = $\frac{\sqrt2}{2}$ $\tan$(45) = $\frac{-1}{1}$ = -1 $\cot$(45) = $\frac{1}{-1}$ = -1 $\csc$(45) = $\frac{\sqrt2}{-1}$ = -$\sqrt2$ $\sec$(45) = $\frac{\sqrt2}{1}$ = $\sqrt2$
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