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: 23


$sin$(480)$^{\circ}$ = $\frac{\sqrt3}{2}$ $cos$(480)$^{\circ}$ = $\frac{-1}{2}$ $tan$(480)$^{\circ}$ = -$\sqrt3$ $cot$(480)$^{\circ}$ = -$\frac{\sqrt3}{3}$ $csc$(480)$^{\circ}$ = $\frac{2\sqrt3}{\sqrt3}$ $sec$(480)$^{\circ}$ = -2

Work Step by Step

480$^{\circ}$ 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. 480$^{\circ}$ - 360$^{\circ}$ = 120$^{\circ}$ Next we find the reference angle: 180$^{\circ}$ - 120$^{\circ}$ = 60$^{\circ}$ $sin$(60)$^{\circ}$ = $\frac{\sqrt3}{2}$ $cos$(60)$^{\circ}$ = $\frac{-1}{2}$ $tan$(60)$^{\circ}$ = $\frac{\sqrt3}{-1}$ = -$\sqrt3$ $cot$(60)$^{\circ}$ = $\frac{-1}{\sqrt3}$ = -$\frac{\sqrt3}{3}$ $csc$(60)$^{\circ}$ = $\frac{2}{\sqrt3}$ = $\frac{2\sqrt3}{\sqrt3}$ $sec$(60)$^{\circ}$ = $\frac{2}{-1}$ = -2
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