Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises: 107

Answer

$\color{blue}{\theta\approx 3.6 \text{ radians}}$

Work Step by Step

RECALL: The area of a sector $(A)$ intercepted by a central angle $\theta$ on a circle whose radius is $r$ is given by the formula: $A = \frac{1}{2}r^2\theta$, where $\theta$ is in radian measure. Substitute the given values of the area and area of the sector to obtain: $A=\frac{1}{2}r^2\theta \\16=\frac{1}{2}(3.0^2)(\theta) \\16=0.5(9)\theta \\16=4.5\theta \\\frac{16}{4.5}=\theta \\3.\overline{5}=\theta \\\color{blue}{\theta\approx 3.6 \text{ radians}}$
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