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Given the graph above, write the equation as a cosine function

A. y = .25 cos ø
B. y = .75 cos 2ø
C. y = -.75 cos 2ø
D. y = -.50 cos 3ø
E. y = cos 4ø

Given the graph above, write the equation as a cosine function A. y = .25 cos ø B-example-1
User KwintenP
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1 Answer

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Answer: Option B


y = 0.75cos(2\phi)

Explanation:

The general cosine function has the following form


y = Acos(b\phi) + k

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


(2\pi)/(b) 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:


A =(0.75-(-0.75))/(2)\\\\A= 0.75

Then
k=0

The cycle is repeated every
\pi units

So the period is
\pi

Thus:


(2\pi)/(b)=\pi\\\\ b=(2\pi)/(\pi)\\\\ b=2

The function is:


y = 0.75cos(2\phi)

when
\phi=0 y is maximum therefore
y=0.75 As shown in the graph

User Kike Gamboa
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7.4k points