Write the equation of the trigonometric graph. Amplitude is 2, Midline is -3, and period is 6 pi. Use cosine function to write the equation.

Answer 1

The general equation for a cosine function is given by:

y = A * cos(B(x - C)) + D

Where:
A = amplitude
B = 2pi / period
C = horizontal shift
D = vertical shift

In this case:
Amplitude (A) = 2
Period = 6pi
Midline = -3

Amplitude (A) = 2
Period = 6pi
Since B = 2pi / period, we can calculate B:
B = 2pi / (6pi) = 1/3

Midline = -3 = D

Since the cosine function has a horizontal shift of 0 (C = 0), we have:

y = 2 * cos((1/3)x) - 3

Therefore, the equation of the trigonometric graph is y = 2 * cos((1/3)x) - 3.