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: 21

Answer

a) $228.6^{\circ} + 360^{\circ}k$ and $311.4^{\circ} + 360^{\circ}k$, for all integers $k$. b) $\theta = 228.6˚, 311.4˚$

Work Step by Step

b) $sin\theta - 3 = 5sin\theta$ $sin\theta - 5sin\theta = 3$ $-4sin\theta = 3$ $sin\theta = -\frac{3}{4}$ $\theta = -48.6˚$ Use $48.6˚$ as the reference angle. And recall that $sin\theta$ is negative in only QIII and QIV. QIII: $\theta = 180 + 48.6$ $\theta = 228.6˚$ QIV: $\theta = 360 - 48.6$ $\theta = 311.4˚$ Therefore, $\theta = 228.6˚, 311.4˚$ a) Take the two angles and add $360^{\circ}k$for all integers $k$, to find all degree solutions. $228.6^{\circ} + 360^{\circ}k$ and $311.4^{\circ} + 360^{\circ}k$, for all integers $k$.
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