Final answer:
To write an equation of a sine function with an amplitude of 2 and a period of 3, you use the formula y(x) = A sin(Bx), where A is the amplitude and B is calculated as 2π divided by the period. So the equation is y(x) = 2 sin((2π/3)x).
Step-by-step explanation:
To write an equation of a sine function with an amplitude of 2 and a period of 3, we use the general form of the sine function:
y(x) = A sin(Bx + C)
where:
- A is the amplitude
- B relates to the period by the formula 2π/period
- C is the phase shift (here we don't have a phase shift given)
Since the amplitude given is 2, A = 2. The period is 3, so we calculate B as 2π/3.
Therefore, the equation of the sine function is:
y(x) = 2 sin((2π/3)x)