Trigonometry 7th Edition

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

Chapter 6 - Section 6.1 - Solving Trigonometric Equations - 6.1 Problem Set: 6

Answer

a) $60^{\circ} + 360^{\circ}k$ and $300^{\circ} + 360^{\circ}k$, for all integers $k$. b) $60^{\circ}, 300^{\circ}$

Work Step by Step

b) Isolate $cos\theta$ $2cos\theta = 1$ $cos\theta = \frac{1}{2}$ Recall knowledge about the unit circle $cos\theta$ is positive in quadrant I and IV - Angles $60˚$ and $300˚$ Therefore, $cos\theta = \frac{1}{2}$ for $\theta = 60˚, 300˚$ a) Take the two angles and add $360^{\circ}k$, for all integers $k$, to find all degree solutions. $60^{\circ} + 360^{\circ}k$ and $300^{\circ} + 360^{\circ}k$, for all integers $k$.
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