Answer:
Maximum: 1, Minimum: -3, Midline y = -1, Amplitude = 4, Period = [tex]\pi[/tex], Frequency [tex]\displaystyle =\frac{1}{\pi}[/tex], equation : [tex]f(x)=-4cos(2x)+1[/tex]
Step-by-step explanation:
Sinusoid Functions
It refers to the oscillating functions like the sine or cosine which range from a minimum and maximum value periodically.
The graph shown can give us all the information we need to answer these questions:
Maximum: 1
Minimum: -3
The midline goes through the center value (mean) of the max and min values, i.e.
Equation of the midline:
[tex]\displaystyle y=\frac{1-3}{2}=-1[/tex]
Amplitude is the difference between the maximum and minimum values
[tex]A=1-(-3)=4[/tex]
The period is the time it takes to complete a cycle. We can see the minimum value is first reached at x=0 and next at [tex]x=\pi[/tex]
Thus the period is
[tex]T=\pi[/tex]
The frequency is the reciprocal of the period:
[tex]\displaystyle f=\frac{1}{T}=\frac{1}{\pi}[/tex]
The angular frequency is
[tex]\displaystyle w=2\pi f=\frac{2\pi }{\pi}=2[/tex]
The equation of the function is a negative cosine (since it starts at the minimum) or a shifted sine or cosine. We'll choose the negative cosine, knowing all the parameters:
[tex]f(x)=-4cos(2x)+1[/tex]
