directions: define the following words below: 1) midline: ___ 2) amplitude: ___ 3) period: ___

Brief Explanations:

1. In the context of periodic - functions (such as sine and cosine functions), the midline is the horizontal line that the graph of the function oscillates around. It is given by (y = D) in the general form of a sinusoidal function (y=A\sin(Bx - C)+D) or (y = A\cos(Bx - C)+D).
2. Amplitude is the maximum displacement from the mid - line of a periodic function. For a sinusoidal function (y = A\sin(Bx - C)+D) or (y=A\cos(Bx - C)+D), the amplitude is (|A|). It represents half of the vertical distance between the maximum and minimum values of the function.
3. The period of a periodic function is the smallest positive value of (p) such that (f(x + p)=f(x)) for all (x) in the domain of the function. For a sinusoidal function (y = A\sin(Bx - C)+D) or (y = A\cos(Bx - C)+D), the period is given by (T=\frac{2\pi}{|B|}).

Answer:

1. Midline: The horizontal line that a periodic function oscillates around.
2. Amplitude: The maximum displacement from the mid - line of a periodic function.
3. Period: The smallest positive value (p) for which (f(x + p)=f(x)) for all (x) in the domain of a periodic function.