Trigonometry (10th Edition)

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

Chapter 3 - Review Exercises - Page 129: 30

Answer

$\theta=0.5$ radian $A= 16$ square units

Work Step by Step

Part 1: To find the central angle $\theta$, we use the formula $s=r\theta$ where $s$ is the arc length, $r$ is the radius and $\theta$ is the central angle in radians. Next, we rearrange the formula to $\theta=\frac{s}{r}$ because $s$ and $r$ are known and $\theta$ is the unknown. Substituting the values of $r=8$ and $s=4$ into the formula and solving: $\theta=\frac{s}{r}=\frac{4}{8}=0.5$ radian Part 2: To find the area of the sector, we use the formula $A=\frac{1}{2}rs$ where $r$ is the radius and $s$ is the arc length. Substituting the values of $r$ and $s$ into the formula and solving: $A=\frac{1}{2}rs=\frac{1}{2}(4)(8)= 16$ square units
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