Chapter 6.4, Problem 107AYU

To determine

Find the role of $\text{a}$ plays in the graph of $\text{f}\left(x\right)=a\sin x$ .

Answer to Problem 107AYU

  $\boxed{\text{Amplitude varies}}$

Explanation of Solution

Given information:

On the screen you will see a slider. Move the point along the slider to see the role $\text{a}$ plays in the graph of $\text{f}\left(x\right)=a\sin x$ .

Calculation:

In the amplitude applets, as a point moves on the slider it generates the graph of sine function $y=a\sin x$ .

So that $A$ represents the amplitude of the sine function that represents the half the distance between maximum and minimum value or height the function attains.

Moving the function along $y-axis$ does not change the amplitude.

It makes the curve of sine function in rectangular pattern. when the radius of the circle $40$ units then curve moves up and down $40$ units along $y-axis$ .

The amplitude represents the energy level, higher the amplitude, higher the energy.

Amplitude can be varied up to $100$ units.

  

the amplitude is the distance from the zero position of the curve.

Hence, $\boxed{\text{Amplitude varies}}$ .