Answer:
The midline is y=-1
Amplitude = 3
The period is 2 units
Step-by-step explanation:
Sinusoidal Function
It refers to a mathematical curve with a smooth and periodic oscillation. Its name comes from the sine function but it can be a cosine function too. They only differ by the phase angle of 90 degrees or π/2 radians.
The amplitude is half the distance from the maximum and the minimum points. The graph shows a sinusoid with a maximum value of y=2 and a minimum value of y=-4.
The amplitude is:
[tex]A=\frac{2+4}{2}=3[/tex]
Amplitude = 3
The midline is the distance from the center of the sinusoid to the x-axis. It's also called the vertical shift.
The midline can be found by subtracting the amplitude A=3 to the maximum value M=2:
ML = 2 - 3 = -1
It can also be found by adding the amplitude to the minimum value:
ML = -4 + 3 = -1
The midline is y=-1
The period is the time the wave takes to complete a full cycle. We only have to focus at any point on the wave (xo,yo) and find the next value of x where the sinusoid has the very same behavior (x1,y1). The period is then x1-x0.
We find at x=0, y=-1 and it's moving up. At x=1 it has the same value but it goes down, so the wave is at its half cycle. At x=2 it repeats the same behavior as for x=0. Thus:
The period is 2 units
