determine the amplitude,period and phase shift of y=-2cos(pix-3)
rewrite it in the most general form
y = -2 cos π(x - 3/π)
amplitude = 2
period = 2π/π = 2
phase shift = 3/π units to the right
To determine the amplitude, period, and phase shift of the given function y = -2cos(pix - 3), we can use the general equation for cosine functions:
y = A*cos(Bx - C) + D
Comparing our given function y = -2cos(pix - 3) to the general equation, we can identify the following values:
Amplitude (A): The amplitude of a cosine function is the absolute value of the coefficient multiplying the cosine term. In this case, the coefficient is -2, so the amplitude is 2.
Period (P): The period of a cosine function is given by the formula 2π/B, where B is the coefficient of x in the cosine term. In this case, B = pi, so the period is 2π/pi or approximately 2.
Phase shift (C): The phase shift of a cosine function is the value of x where the cosine function is at its maximum or minimum value. To find the phase shift, we solve the equation Bx - C = 0 for x. In this case, B = pi and C = 3. So, pi*x - 3 = 0, and solving for x gives x = 3/pi (or approximately 0.954).
Therefore, the amplitude is 2, the period is 2, and the phase shift is 3/pi.