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: 90


$s=7.854\, cm$ $A= 35.343 \, cm^2$

Work Step by Step

$\because s = r \theta$ $\because A = \dfrac{1}{2}r^2 \theta$ 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 $\theta$ Converting $\theta$ from degrees to radians gives: $$\theta = 50 \times \dfrac{\pi}{180}= \dfrac{5 \pi}{18} \text{ radians}$$ Using the formulas above, we obtain: $s=r \theta = 9 \times \dfrac{5\pi}{18} \approx \boxed{7.854 \, cm}$ $A = \dfrac{1}{2}r^2 \theta = \dfrac{1}{2} \times (9)^2 \times \dfrac{5\pi}{18} \approx \boxed{35.343 \, cm^2}$
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