Answer:
y = 4 sin(2x/3)
Explanation:
The parent function for sine functions is: y = a sin b(x - c) + d
"a" defines amplitude/vertical dilation
"b" defines the change to the period/horizontal dilation
"c" defines the phase shift/horizontal translation
"d" defines the midline/vertical translation
We can already set "a = 4" because 4 is the amplitude.
However, to include the period into the function, we have to take note of the parent sine function already having a period of 2π.
This means: 2π/b = period
2π/period = b
2π/3π = b
2/3 = b
Knowing the "a" and "b" values, we can set up the equation:
y = 4 sin(2x/3)
No horizontal/vertical translations were applied, so "c" and "d" are both zero.