Answer:
[tex]b. \ y=3cos(3\theta)[/tex]
Step-by-step explanation:
The cosine function is a trigonometric function whose curve is symmetric with respect to the y-axis, hence this function is said to be even. This function has the following form:
[tex]y=acos(b \theta)[/tex]
The amplitude of the plotted graph is 3 that represents half the distance between the maximum and minimum values. Since at x = 0, y = 3, this y-value is the value of a. On the other hand, the period, which is the length of one cycle of the curve, can be found as [tex]T=\frac{2\pi}{3}[/tex] and:
[tex]T=\frac{2\pi}{b} \therefore b=\frac{2\pi}{T}=\frac{2\pi \times 3}{2\pi}=3[/tex]
Finally:
[tex]\boxed{y=3cos(3\theta)}[/tex]
