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Write a cosine function for the graph.

a.
y= 4 cos 2theta
c.
y= -4 cos 2theta
b.
y= 4 cos theta/2
d.
y= -4 cos theta/2

Write a cosine function for the graph. a. y= 4 cos 2theta c. y= -4 cos 2theta b. y-example-1

1 Answer

3 votes

Answer:

Correct answer: y= 4 cos 2theta

Explanation:

The Cosine Function

The general form of the cosine is


Y=A.cos(w\theta+B)

where A is the amplitude, w is the angular frequency and B is the phase shift

The amplitude is the positive top value of the sinusoid or the most negative value. Since the sinusoid goes from -4 to 4, the amplitude is 4, thus


Y=4cos(w\theta+B)

To find B and w, we use two points from the graph (0,4) and
(\pi/4,0):


4=4cos(w*0+B)

Simplifying


1=cosB

Thus B=0

Now for the second point


0=4cos(w* \pi/4)

Or equivalently


\displaystyle (\pi w)/(4)=(\pi)/(2)

Thus

w=2

Then, the cosine function is


Y=4cos2\theta

Correct answer: y= 4 cos 2theta

User Ewbi
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