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 - Page 131: 14


(a) Refer to the drawing of the angle in the attached image below. (b) $\dfrac{3}{4}\pi$ radians (c) reference angle = $\color{blue}{45^o=\dfrac{\pi}{4}}$ radians.

Work Step by Step

(a) From the positive x-axis, move 135 degrees counter clockwise. (refer to the attached image above for the drawing) (b) Convert to radians by multiplying $\dfrac{\pi}{180^o}$ to obtain: $135^o \cdot \dfrac{\pi}{180^o} = \dfrac{3}{4}\pi$ radians (c) The angle is in Quadrant II. The reference angle of an angle $\theta$ in Quadrant I can be found using the formula $=180^o- \theta$. Thus, the reference angle of the given angle is: $180^0-135^0 = \color{blue}{45^o=\dfrac{\pi}{4}}$ radians.
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