Answer:
Correct answer: y= 4 cos 2theta
Step-by-step explanation:
The Cosine Function
The general form of the cosine is
[tex]Y=A.cos(w\theta+B)[/tex]
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
[tex]Y=4cos(w\theta+B)[/tex]
To find B and w, we use two points from the graph (0,4) and [tex](\pi/4,0)[/tex]:
[tex]4=4cos(w\times0+B)[/tex]
Simplifying
[tex]1=cosB[/tex]
Thus B=0
Now for the second point
[tex]0=4cos(w\times \pi/4)[/tex]
Or equivalently
[tex]\displaystyle \frac{\pi w}{4}=\frac{\pi}{2}[/tex]
Thus
w=2
Then, the cosine function is
[tex]Y=4cos2\theta[/tex]
Correct answer: y= 4 cos 2theta
