how do i find the amplitude, period, phase shift of y=2 cos(-4t-(-4 pi/3))

The amplitude is the number "2" in front of the trig function.

The frequency (f) is obtained by setting the number "4" in front of "t" equal to 2 pi f. Then solve for f. You can ignore the minus sign.

The phase shift is the 4pi/3 in the inner arentheses. It would be negative if there were a + in front of t, but in this case it is positive.

To find the amplitude, period, and phase shift of a given cosine function, you can follow these steps:

1. Amplitude: The amplitude represents the maximum displacement from the mean or average value. In this case, the coefficient of the cosine function is 2, so the amplitude is simply 2.

2. Period: The period represents the length of one complete cycle of the function. For a cosine function with the general form y = A cos(Bx + C), the period can be calculated using the formula T = 2π/B. In this case, the coefficient of t (which is -4) corresponds to B in the general form. Thus, the period is T = 2π/(-4) = -π/2.

3. Phase Shift: The phase shift represents the horizontal translation of the function. To find the phase shift, you need to isolate the constant term inside the parentheses in the cosine function. In this case, the phase shift is (-4π/3).

Therefore, for the given function y = 2cos(-4t - (-4π/3)), the amplitude is 2, the period is -π/2, and the phase shift is -4π/3.