Respuesta :

luisejr77

Answer: Option A

The Amplitude is

[tex]A = \frac{1}{2}[/tex]

Then the period is

[tex]\frac{2}{3}\pi[/tex]

Step-by-step explanation:

The general sine function has the following form  

[tex]y = Asin(bx) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

In this case we have the following function

[tex]f(t)=\frac{1}{2}sin(3t)[/tex]

Thus:

[tex]b=3[/tex]

Then the period is

[tex]\frac{2\pi}{3}=\frac{2}{3}\pi[/tex]

The Amplitude is

[tex]A = \frac{1}{2}[/tex]

The answer is Option A

BasketballEinstein

Answer:

a. amplitude: [tex]\displaystyle \frac{1}{2};[/tex]period: [tex]\displaystyle \frac{2}{3}\pi[/tex]

Explanation:

[tex]\displaystyle f(t) = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{3}\pi \\ Amplitude \hookrightarrow \frac{1}{2}[/tex]

With the above information, you now should have an idea of how to interpret graphs like this.

I am joyous to assist you at any time.