Write an equation of the sine function with amplitude 9 period 3 pi

The a in front of Sin is the amplitude and the period is 2pi/k.

To get a period of 3pi, set up an equation. 3pi = 2pi/k and solve for k.

3pi = 2pi/k

Multiply k on both sides.

k * 3pi = 2pi

Divide both sides by 3pi

k = 2pi/3pi; k = 2/3

y = 9Sin (2/3) x