Chapter 8.5, Problem 1AYU

The amplitude A and period $T$ of $f\left(x\right)=5\sin \left(4x\right)$ are __ and ___. (pp. 412—414)

To determine

To find: Amplitude $\text{A}$ and period $\text{T}$.

Answer to Problem 1AYU

Solution:

The amplitude and period of given $\text{f}(\text{x})$ are 5 and $\frac{\text{π}}{2}$.

Explanation of Solution

Given:

$f\left(x\right) = 5\text{sin}\left(4x\right)$

Formula used:

$f\left(x\right) = A\text{sin}\left(wt\right)$

Calculation:

We know that $\text{T}$ is $\frac{2\pi }{w}$.

So $T = \frac{2\pi }{4} = \frac{\pi }{2}$

Amplitude given by

$f\left(x\right) = A\text{sin}\left(wt\right)$

So $\text{A} = 5$

Amplitude is 5