Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises - Page 51: 20


(a) $\sin$ 38$^{\circ}$ (b) $\cot$ 19$^{\circ}$ (c) $\csc$ 66$^{\circ}$

Work Step by Step

The cofunction uses Trigonometric Identities to show the relationship between Trigonometric Functions. Below shows the following relationship between common functions: $\sin$(90$^{\circ}$ - x) = $\cos$ x $\cos$(90$^{\circ}$ - x) = $\sin$ x $\tan$(90$^{\circ}$ - x) = $\cot$ x $\cot$(90$^{\circ}$ - x) = $\tan$ x $\sec$(90$^{\circ}$ - x) = $\csc$ x $\csc$(90$^{\circ}$ - x) = $\sec$ x Therefore: (a) $\cos$ 52$^{\circ}$ = $\sin$(90$^{\circ}$ - 52$^{\circ}$) = $\sin$ 38$^{\circ}$ (b) $\tan$ 71$^{\circ}$ = $\cot$(90$^{\circ}$ - 71$^{\circ}$) = $\cot$ 19$^{\circ}$ (b) $\sec$ 24$^{\circ}$ = $\csc$(90$^{\circ}$ - 24$^{\circ}$) = $\csc$ 66$^{\circ}$
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