What is an equation for a sine curve with amplitude 2 and period 4 pi radians?

We will be using the phase shift standard form to solve this.

Answer: The equation for a sine curve with amplitude 2 and period 4 pi radians is f(x) = 2 sin(x/2).

Let's solve this step by step.

Explanation:

Given that, Amplitude = 2 and Time Period = 4π

We have a standard form for phase shift:

f(x) = a sin(bx + c) + d

Where, Amplitude = a, Time Period = 2π/b, Phase Shift = c, Vertical Shift = d.

On Comparing we get: a = 2, b = 1/2, c = 0, d = 0.

⇒ f(x) = 2 sin(x/2)

Hence, the equation for a sine curve with amplitude 2 and period 4 pi radians is f(x) = 2 sin(x/2).