Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.2 - Radians and Degrees - 3.2 Problem Set: 19

Answer

(a) Refer to the image below for the drawing. (b) $\dfrac{7}{3}\pi$ radians (c) Reference angle = $60^o$ or $\dfrac{\pi}{3}$ radians.
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Work Step by Step

(a) From the positive x-axis, move 420 degrees counter clockwise. Note that the terminal side of this angle is the same as the terminal side of a 60-degree angle. (refer to the attached image above for the drawing) (b) Convert to radians by multiplying $\dfrac{\pi}{180^o}$ to obtain: $420^o \cdot \dfrac{\pi}{180^o} = \dfrac{7}{3}\pi$ radians (c) The angle is in Quadrant I as it is coterminal with $60^o$. The reference angle of an angle $\theta$ in Quadrant I is itself. Thus, the reference angle of the given angle is: $\color{blue}{60^o}=60^o \cdot \dfrac{\pi}{180^o}=\color{blue}{\dfrac{\pi}{3}}$ radians.
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