To create a sine function with an amplitude of 2/3, a period of 4π, and a phase shift of π/2, the correct equation is derived from the standard sine function format. The period affects the coefficient of the variable inside the sine function, which is calculated as 2π divided by the period, resulting in a coefficient of 1/2. The phase shift is incorporated by adjusting the angle inside the sine function accordingly. Therefore, the final equation should be y = (2/3) sin(1/2Θ - π/2). Understanding the definitions of period and phase shift is crucial for correctly formulating the sine function.
