Question

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

Answer 1

Answer: Option B

$y = 0.75cos(2\phi)$

Step-by-step 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.  

$\frac{2\pi}{b}$ 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:  

$A =\frac{0.75-(-0.75)}{2}\\\\A= 0.75$

Then $k=0$

The cycle is repeated every $\pi$ units  

So the period is $\pi$

Thus:

$\frac{2\pi}{b}=\pi\\\\ b=\frac{2\pi}{\pi}\\\\ b=2$

The function is:

$y = 0.75cos(2\phi)$

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