The equation of a sine curve can be formulated with parameters that define its amplitude and period. In this case, we are looking for a sine function with an amplitude of 2 and a period of 4π radians.
The general form of the sine function is:
y = A * sin(B(x - C)) + D
Where:
- A is the amplitude of the wave,
- B affects the period of the wave,
- C is the horizontal shift, and
- D is the vertical shift.
In our case:
- The amplitude A is 2, so we have A = 2.
- The period P is given by the formula P = 2π/B. We want the period to be 4π, so:
4π = 2π/B
Solving for B gives:
B = 2π/(4π) = 1/2
Now, substituting these values into the sine function, we get:
y = 2 * sin((1/2)x)
This is the equation of the sine curve with an amplitude of 2 and a period of 4π radians. The equation can also be written as:
y = 2 * sin(0.5x)
And that gives us the sine curve we were looking for!