ANSWER
C.
[tex]f(t) = - 3 \sin(3t) [/tex]
EXPLANATION
The given function has range:
-3≤f(t)≤3
This implies that, the amplitude is
[tex] |a| = 3[/tex]
The function is symmetric with respect to the origin so this is a sine function.
This function is again reflected in the x-axis, hence
a=-3.
The period of this function is
[tex] \frac{2\pi}{b} = \frac{2\pi}{3}[/tex]
This implies that, b=3,
hence the equation of the function is
[tex]f(t) = - 3 \sin(3t) [/tex]
