Write the equation of the trigonometric graph. Amplitude is 2, Midline is -3, and period is 6pi.
The general form of a trigonometric equation is \[y = A \sin(B(x-h)) + k,\] where A is the amplitude, B determines the period, h is the horizontal shift, and k is the vertical shift.
Given that the amplitude is 2, the midline is -3, and the period is $6\pi$, we can substitute these values into the general form. Hence, our equation becomes \[y = 2\sin\left(\frac{2\pi}{6\pi}\left(x-0\right)\right) -3.\]
Simplifying further, we find that the equation of the graph is \[y = 2\sin\left(\frac{1}{3}x\right) -3.\]