Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.5 - Graphs of Sine and Cosine Functions - Exercise Set - Page 595: 6

Answer

The amplitude of the function is $4$.

Work Step by Step

We have the trigonometric function $y=-4\sin x$ The amplitude is the maximum value of $y$. The maximum value of the given trigonometric function is $\left| -4 \right|$. Thus , te amplitude of the trigonometric function is $4$. The period of the trigonometric function is $2\pi $. And the quarter period is $\frac{2\pi }{4}$ or $\frac{\pi }{2}$. The cycle begins at $x=0$. Add quarter periods to find out the key points. First key point is ${{x}_{1}}=0$ Second key point is $\begin{align} & {{x}_{2}}=0+\frac{\pi }{2} \\ & =\frac{\pi }{2} \end{align}$ Third key point is $\begin{align} & {{x}_{3}}=\frac{\pi }{2}+\frac{\pi }{2} \\ & =\pi \end{align}$ Fourth key point is $\begin{align} & {{x}_{4}}=\pi +\frac{\pi }{2} \\ & =\frac{3\pi }{2} \end{align}$ Fifth key point is $\begin{align} & {{x}_{5}}=\frac{3\pi }{2}+\frac{\pi }{2} \\ & =2\pi \end{align}$
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