Precalculus (6th Edition) Blitzer

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

Chapter 4 - Review Exercises - Page 645: 72

Answer

The amplitude of the function is $1$ and period is $2$.

Work Step by Step

The given equation is in the form of $y=A\sin Bx$. Here, $A=-1\text{ and }B=\pi $ So, the amplitude is: $\begin{align} & \text{Amplitude=}\left| A \right| \\ & =\left| -1 \right| \\ & =1 \end{align}$ The period is: $\begin{align} & \text{Period = }\frac{2\pi }{B} \\ & =\frac{2\pi }{\pi } \\ & =2 \end{align}$ $\text{Phase shift=}\frac{C}{B}=0$ And the quarter period is as follows: $\begin{align} & \text{Quarter-period}=\frac{2}{4} \\ & =\frac{1}{2} \end{align}$ Now, add quarter periods starting from $x=\text{0}$ to generate x-values for the key points. The x-value for the first key point is as follows: $x=\text{0}$ And the x-value for the second key point is: $\begin{align} & x=0+\frac{1}{2} \\ & =\frac{1}{2} \end{align}$ And the x-value for the third key point is: $\begin{align} & x=\frac{1}{2}+\frac{1}{2} \\ & =1 \end{align}$ And the x-value for the fourth key point is: $\begin{align} & x=1+\frac{1}{2} \\ & =\frac{3}{2} \end{align}$ And the x-value for the fifth key point is: $\begin{align} & x=\frac{3}{2}+\frac{1}{2} \\ & =2 \end{align}$
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