Write an equation of the sine function with amplitude 3, period 3ð/2, and phase shift ð/4.

Is it y= 3sin(4x/3-ð/3)?

yes,

I used to encourage my students to have the period as a factor outside the bracket, such as

y = 3 sin (4/3)(x - pi/4)

the properties of the curve are immediately visible.
notice if you expand my equation, you get yours.

To write an equation of a sine function with the given characteristics, we can use the following general form:

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

where:
A represents the amplitude,
B represents the reciprocal of the period,
C represents the phase shift, and
D represents the vertical shift.

Given the specific characteristics:
Amplitude = 3
Period = 3π/2
Phase shift = π/4

We can substitute these values into the general form:

y = 3 * sin(B(x - π/4)) + D

To find the value of B, we use the relationship between period and B, which is reciprocal. In this case, the period is 3π/2, so:

B = 2π / (3π/2)
= 4/3

Substituting this into the equation:

y = 3 * sin((4/3)(x - π/4)) + D

Now we need to find the value of D, which is the vertical shift. The sine function has a vertical midpoint at y = 0, so the vertical shift is 0.

Therefore, the equation of the sine function is:

y = 3 * sin((4/3)(x - π/4))