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: 10


The amplitude and period of the function are $2$ and $8\pi $ , respectively.

Work Step by Step

We have the trigonometric function $y=2\sin \frac{1}{4}x$ The amplitude is the maximum value of $y$. The maximum value of the given trigonometric function is $2$. So, the amplitude of the trigonometric function is $2$. The function after a certain interval starts repeating itself, and this interval is known as the period of the function. And the period $\left( B \right)$ of the trigonometric function is $\begin{align} & B=\frac{2\pi }{\left( \frac{1}{4} \right)} \\ & =8\pi \end{align}$ And the quarter period is $\frac{8\pi }{4}$ or $2\pi $. 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 $\begin{align} & {{x}_{2}}=0+2\pi \\ & =2\pi \end{align}$ Third key point is $\begin{align} & {{x}_{3}}=2\pi +2\pi \\ & =4\pi \end{align}$ Fourth key point is $\begin{align} & {{x}_{4}}=4\pi +2\pi \\ & =6\pi \end{align}$ Fifth key point is $\begin{align} & {{x}_{5}}=6\pi +2\pi \\ & =8\pi \end{align}$
Small 1571730398
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.