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: 99


$\omega=\frac{1}{60}\text{ rad/s}$ $v=\frac{1}{12} \text{ cm/s}$

Work Step by Step

Identify the given: $\theta=\frac{1}{3} $ $t=20 \text{ s}$ $r=5\text{ cm}$ Solve for the angular speed using the formula$\omega=\frac{\theta}{t}$ to obtain: $$\omega=\frac{\frac{1}{3}\text{ radians}}{20\text{ s}}=\frac{1}{60}\text{ rad/s}$$ Solve for the linear speed using the formula $v=r\omega$ to obtain: $$v=5\text{ cm}\times\frac{1}{60}\text{ rad/s}=\frac{1}{12}\text{ cm/s}$$
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