Question

What is the equation of a sine function with an amplitude of 2 and a period of 4π?

a. y=2sin(2x)
b. y=sin(4πx)
c. y=2sin(x)
d. y=sin(4πtx)

Answer 1

The equation of a sine function with an amplitude of 2 and a period of 4π is y = 2sin(x).

Step-by-step explanation:

The equation of a sine function with an amplitude of 2 and a period of 4π is y = 2sin(x) (option c).

The general equation of a sine function is y = A sin(Bx + C), where A is the amplitude, B determines the period, and C represents any phase shift.

In this case, the amplitude is 2, so A = 2. The period is 4π, so B = 2π/4π = 1/2. There is no phase shift, so C = 0.

Substituting the values into the general equation, we get y = 2sin(x).