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

Question

asked Jul 27, 2020 221k views

1 Answer

Kike Gamboa · Answer 1 · 2020-08-03T12:20:46+0000

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