Question

What is the equation of a sine function with an amplitude of 2 and a period of 4(3.14, pi)

1. Y=1/2sin(2x)
2.Y= 1/2sin(4 3.14x)
3. Y= 2sin (1/2x)
4. Y= 2sin (4 3.14x)

Answer 1

The correct equation of a sine function with an amplitude of 2 and a period of 4π is Y = 2sin(1/2x). This is option 3 from the provided choices.

Step-by-step explanation:

The equation of a sine function with an amplitude of 2 and a period of 4π (approximately 12.56) is y = 2sin(π/2x). Considering that the standard form of a sine function is y = Asin(Bx), the amplitude is given by the coefficient A, and the period is 2π/B. Therefore, for a period of 4π, B must equal 1/2, as the period is equal to 2π/B, which gives 2π/(1/2) = 4π. Thus, option 3, Y = 2sin(1/2x), is the correct choice as it has the required amplitude and period.