Question

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

Answer 1

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