Final answer:
The period of the function y = -2sin(2/3x - 4) is 3π. The period is calculated by the formula 2π divided by the absolute value of the coefficient of x inside the sine function. Therefore, the correct option is b) 3∏.
Step-by-step explanation:
The period of a trigonometric function such as y = -2sin(2/3x - 4) can be determined by looking at the coefficient of x inside the sine function.
This coefficient affects the frequency of the sine wave, which is the reciprocal of the period. For the function sin(bx), the period is given by 2π / |b|.
For the function given in the question, y = -2sin(2/3x - 4), the coefficient b of x is 2/3. Therefore, the period P is found by dividing 2π by |2/3|, which equals 3π. So the period of the function is 3π. Therefore, the correct option is b) 3∏.