Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.2 Trigonometric Equations I - 6.2 Exercises - Page 274: 68a


To produce voltage $E=0$, it takes at least 2 seconds.

Work Step by Step

$$E=20\sin(\frac{\pi t}{4}-\frac{\pi}{2})$$ Since $t$ is time in seconds, the range of $t$ is $[0,\pi)$ For $E=0$, we get the equation $$20\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$ $$\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$ For $\frac{\pi t}{4}-\frac{\pi}{2}=0$, we would get $\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$. Also we would get the least positive $t$ through this. $$\frac{\pi t}{4}-\frac{\pi}{2}=0$$ $$\frac{\pi t}{4}=\frac{\pi}{2}$$ $$t=\frac{\pi}{2}\times\frac{4}{\pi}$$ $$t=2(seconds)$$ So to produce voltage $E=0$, it takes at least 2 seconds.
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