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 - Page 325: 16

Answer

$(a)\quad t=k\pi$ $(b) \quad 0$ and $\pi.$

Work Step by Step

The first task is to isolate the trigonometric function on one side: Add $(-4)$ to both sides... $3\sin t=4-4\qquad $ ... simplify $ 3\sin t=0\quad$ ... divide with $3$ $\sin t=0$ Now, we find a reference angle. From the table of characteristic angles, we know that $\sin 0=0.$ Next, we know that within the interval $0\leq t \lt 2\pi $ the radian angles that satisfy the equation are $0$ and $\pi.$ Finally, to each individual solution, add multiples of $ 2\pi$ to cover all solutions: $(a)$ $ t=0+2k\pi$ or $ t=\pi+2k\pi$ which can be combined and written as $ t=k\pi$ $(b)$ The solutions within the interval $0\leq t \lt 2\pi:$ $0$ and $\pi.$
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