Question

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

Answer 1

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