Find the amplitude, period, and phase shift of y=-2cosx
The general form of the cosine function is y = A*cos(B(x-C)) + D, where A is the amplitude, B is the coefficient of x (which affects the period), C is the phase shift, and D is the vertical shift.
In this case, the given function is y = -2*cos(x).
Comparing it to the general form, we can see that:
- The amplitude (A) is 2. Since the coefficient of cos(x) is -2, the amplitude is the absolute value of -2, which is 2.
- The period (P) is 2π. In this case, B = 1, so the period is 2π/B = 2π/1 = 2π.
- The phase shift (C) is 0. In this case, there is no coefficient affecting x in the function, so the phase shift is 0.
Therefore, the amplitude is 2, the period is 2π, and the phase shift is 0 for y = -2*cos(x).