Final answer:
The range of y = 2/3 sin x for pi < x < 3pi/2 is -2/3 < y < 0.
Step-by-step explanation:
The range of the function y = 2/3 sin x, where pi < x < 3pi/2, can be determined by finding the maximum and minimum values of the sine function within the given interval.
When the input of the sine function is between pi and 3pi/2, the values of sine are negative. Therefore, the maximum value of the function is -2/3 and the minimum value is 0. So, the range of y = 2/3 sin x for pi < x < 3pi/2 is -2/3 < y < 0.