Trigonometry (10th Edition)

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

Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises: 61

Answer

$\cos\theta=\frac{-4}{5}$

Work Step by Step

1.We get this information from the sine value $y=3$ $r=5$ 2. We can use y and r to find x (we need to remember that sign of x depends on quadrant, since it ends in quadrant II, x must be negative) $r=\sqrt {x^{2}+y^{2}}$ $x=-\sqrt {r^{2}-y^{2}}=-\sqrt {5^{2}-3^{2}}=-\sqrt {25-9}=-\sqrt {16}=-4$ 3.Then insert values, $\cos\theta=\frac{-4}{5}$
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