Final answer:
A sine equation with an amplitude of 1/2 and a period of 2π/3 is y(x) = (1/2) sin(3x), where the coefficient 3 is found from the relationship (2π)/B = period.
Step-by-step explanation:
To write a sine equation with a given amplitude and period, the general form used is y(x) = A sin(Bx + C), where A is the amplitude and (2π)/B is the period.
In this case, the amplitude is 1/2 and the period is 2π/3. To find the value of B, we use the relationship between period and B: (2π)/B = 2π/3 ⇒ B = 3.
Thus, the sine equation with the given amplitude (1/2) and period (2π/3) is:
y(x) = (1/2) sin(3x).