Determine the amplitude, period, and phase shift for -cos(x/2)+3
The equation is in the form y = A*cos(B(x - C)) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.
For the given equation, y = -cos(x/2) + 3:
Amplitude (A): The magnitude of the coefficient of the cosine term is 1, so the amplitude is |1| = 1.
Period (B): The period of the cosine function is determined by B in the equation. Since B = 1/2, the period is 2π/B = 2π/(1/2) = 4π.
Phase Shift (C): The formula for the phase shift is (C * B), so the phase shift is C = 0.
Vertical Shift (D): The equation is y = -cos(x/2) + 3, so the vertical shift is D = 3.
Therefore, the amplitude is 1, the period is 4π, and the phase shift is 0 for the given equation.