Answer:
Maximum value :
It is the peak value of the sine wave from the origin along the positive y axis
In the given sine wave the Maximum value is 1
Minimum value :
It is the peak value of the sine wave from the origin along the negative y axis
In the given sine wave the Maximum value is -3
Midline :
It is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.
Here in the given graph the mid line is y = -1
since the maximum and minimum points are 1 and -3 respectively
Amplitude:
The vertical distance between the mid-line and one of the extremum points.
From the graph , the amplitude is 2
Period:
The distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).
In the graph the period is [tex]\pi[/tex]
Frequency:
Frequency is the number of cycles in a unit of time
Frequency =[tex]\frac{1}{period}[/tex]
Frequency = [tex]\frac{1}{\pi}[/tex]
Equation of the graphed function:
The general equation of the sine wave is
[tex]y(t) = Asin(\omega t + \psi)[/tex]
where
A is the amplitude
[tex]\omega[/tex] is the angular frequency and is equal to [tex]2\pi f[/tex]
f is the frequency
t is the time
[tex]\psi[/tex] is the phase
Now substituting the values we gte
[tex]y(t) = 2sin(2t +\psi)[/tex]
