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: 20

Answer

$sin$(315) = $\frac{-\sqrt2}{2}$ $cos$(315) = $\frac{\sqrt2}{2}$ $tan$(315) = -1 $cot$(315) = -1 $sec$(315) = -$\sqrt2$ $sin$(315) = $\sqrt2$

Work Step by Step

315$^{\circ}$ We can solve for the functions by using the coterminal angle. We can find the coterminal angle by adding or subtracting 360$^{\circ}$ as many times as needed. 300$^{\circ}$ - 360$^{\circ}$ = -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 $sec$(-45) = $\frac{\sqrt2}{-1}$ = -$\sqrt2$ $sin$(-45) = $\frac{\sqrt2}{1}$ = $\sqrt2$
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