Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.1 Angles and Their Measures - 5.1 Assess Your Understanding - Page 386: 83


$0.24 \text{ radians}$

Work Step by Step

$\because A = \dfrac{1}{2}r^2 \theta$ where $r$: Radius of the circle $\theta$: Central angle that subtends the arc (in radians) $A$: Area of the sector of the circle formed by the central angle $\theta$ Derive the formula for $\theta$: \begin{align*} A&=\frac{1}{2}r^2\theta\\\\ 2A&=r^2\theta\\\\ \dfrac{2A}{r^2}&=\theta\\\\ \end{align*} Using this formula gives: $\theta = \dfrac{2A}{r^2}$ $\theta = \dfrac{2\times 3}{5^2} = \boxed{0.24 \text{ radians}}$
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