509 rounded to the nearest hundred would be 500
ANSWER
C.

EXPLANATION
The given function has range:
-3≤f(t)≤3
This implies that, the amplitude is

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

This implies that, b=3,
hence the equation of the function is

Answer:

Step-by-step explanation:

Multiply cos(x) by 1:

Factor out cos(x):

Apply the pythagorean identity (
):

Rewrite
:

Cancel cos(x):

Rewrite:

Answer:
y = 0.5cos(4(x+π/2)) -2
Step-by-step explanation:
The centerline of the oscillation is at -2, so only the 2nd and 4th choices are viable.
The multiplier of x is computed from (2π)/period. One period is π/2, so the multiplier of x is ...
... 2π/(π/2) = 4 . . . . . matching the 2nd selection.
The horizontal offset in the second equation (π/2) is of no consequence, as it is one full period of the function.
The peak-to-peak amplitude of the oscillation is 1 unit, so the multiplier of the cosine function (which usually has a peak-to-peak value of 2 units) is 0.5. Every offered answer has that characteristic.
The appropriate choice is the 2nd one:
... y = 0.5cos(4(x+π/2)) -2