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 387: 94


$4.71\text{ cm}^{2}$

Work Step by Step

We have: radius $r=3\text{ cm}$ central angle $\theta=60^{\circ}=\frac{\pi}{3}\text{ radians}$ The area of a sector is given by the formula $A=\frac{1}{2}r^{2}\theta$. Use this formula to obtain: $A=\frac{1}{2}\times (3\text{ cm})^{2}\times \frac{\pi}{3}$ $A=\frac{3\pi}{2}\text{ cm}^{2}\approx4.71\text{ cm}^{2}$ Thus, the area of the sector rounded to two decimal places is $4.71\text{ cm}^{2}$.
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