Complete the general form of the equation of a sinusoidal function having an amplitude of 4, a period of π, and a phase shift to the right 2 units.y =

To find the general form of the equation of a sinusoidal function, we need to consider the given information: amplitude, period, and phase shift.

1. Amplitude: The amplitude of a sinusoidal function represents the maximum distance from the midline to the peak or trough of the graph. In this case, the amplitude is given as 4.

2. Period: The period of a sinusoidal function is the distance between two consecutive peaks or troughs. In this case, the period is given as π.

3. Phase Shift: The phase shift represents the horizontal shift of the graph. A positive phase shift indicates a shift to the right, while a negative phase shift indicates a shift to the left. In this case, the phase shift is to the right by 2 units.

Now, let's use this information to determine the general form of the equation.

The general form of a sinusoidal function is given as: y = A * sin(B(x - C)) + D

Where: A represents the amplitude, B represents the frequency (B = 2π/period), C represents the phase shift, and D represents the vertical shift (if any).

Using the given information, we can substitute the values into the general form:

A = 4 (amplitude) Period = π (period) Phase shift = 2 (shift to the right)

Amplitude (A) = 4 Frequency (B) = 2π/Period = 2π/π = 2 Phase shift (C) = -2 (negative because it is a shift to the right) Vertical shift (D) = 0 (no vertical shift mentioned)

Substituting these values into the general form, we get:

y = 4 * sin(2(x - (-2))) + 0

Simplifying further:

y = 4 * sin(2(x + 2))

Therefore, the general form of the equation of the given sinusoidal function is y = 4 * sin(2(x + 2)).