Answer: Option B
[tex]y = 0.75cos(2\phi)[/tex]
Step-by-step explanation:
The general cosine function has the following form
[tex]y = Acos(b\phi) + 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.
The maximum value of y is is 0.75 and the minimum is -0.75. Then the amplitude A is:
[tex]A =\frac{0.75-(-0.75)}{2}\\\\A= 0.75[/tex]
Then [tex]k=0[/tex]
The cycle is repeated every [tex]\pi[/tex] units
So the period is [tex]\pi[/tex]
Thus:
[tex]\frac{2\pi}{b}=\pi\\\\ b=\frac{2\pi}{\pi}\\\\ b=2[/tex]
The function is:
[tex]y = 0.75cos(2\phi)[/tex]
when [tex]\phi=0[/tex] y is maximum therefore [tex]y=0.75[/tex] As shown in the graph
