Chapter 6.4, Problem 35E

To determine

To find: the amplitude and period of the function.

Answer to Problem 35E

Amplitude: 0.5

Period: $\frac{1}{349}$

Explanation of Solution

Given information:

  $y=0.5\sin 698\pi t$

Calculation:

The general equation for sine function is as follows:

  $y=A\sin k\theta$

Here, $A$ is coefficient of absolute value of amplitude and $k$ is absolute value of coefficient of $\theta$ .

Compare the given equation to the general equation to get the values of $A\text{ and }k$ as 0.5 and $2\pi$ .

The value of amplitude can be evaluated as follows:

  $\begin{array}{c}\text{Amplitude}=\left|A\right|\\ =\left|0.5\right|\\ =0.5\end{array}$

The value of period can be evaluated as follows:

  $\begin{array}{c}\text{Period}=\frac{2\pi }{k}\\ =\frac{2\pi }{698\pi }\\ =\frac{1}{394}\end{array}$

Thus, the value of an amplitude is 0.5 and the value of period is $\frac{1}{349}$ .