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: 12

Answer

c = 5 $\sin$$B$ = $\frac{4}{5}$ $\cos$$B$ = $\frac{3}{5}$ $\tan$$B$ = $\frac{4}{3}$ $\csc$$B$ = $\frac{5}{4}$ $\sec$$B$ = $\frac{5}{3}$ $\cot$$B$ = $\frac{3}{4}$

Work Step by Step

Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$ c$^{2}$ = 3$^{2}$ + 4$^{2}$ c$^{2}$ = 9 + 16 c$^{2}$ = 25 c = $\sqrt 25$ c = 5 $\sin$$B$ = $\frac{opposite}{hypotenuse}$ = $\frac{b}{c}$ = $\frac{4}{5}$ $\cos$$B$ = $\frac{adjacent}{hypotenuse}$ = $\frac{a}{c}$ = $\frac{3}{5}$ $\tan$$B$ = $\frac{opposite}{adjacent}$ = $\frac{b}{a}$ = $\frac{4}{3}$ $\csc$$B$ = $\frac{hypotenuse}{opposite}$ = $\frac{c}{b}$ = $\frac{5}{4}$ $\sec$$B$ = $\frac{hypotenuse}{adjacent}$ = $\frac{c}{a}$ = $\frac{5}{3}$ $\cot$$B$ = $\frac{adjacent}{opposite}$ = $\frac{a}{b}$ = $\frac{3}{4}$
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