Trigonometry functions like sine and cosine can be represented by equations involving amplitude (A), period (T), and phase shift (C). The amplitude is the distance from the midpoint to the highest/lowest point, the period is the distance between repeating points, and the phase shift represents horizontal displacement from the original position. These properties, along with a shift (D) in the y-value, determine the shape and position of the resulting wave graph.

1. Trigonometry

2. The period (T) is the distance between any two repeating points on the function. (2π/b = period)
The amplitude (A) is the distance from the midpoint to the highest or lowest point of the function.
(|a| = amp)
Phase shift is the amount of horizontal displacement of the function from its original position.
(c/b = phase shift)
Sine Function y = Asin(Bx + C) + D
Cosine Function y = Acos(Bx + C) + D
Properties

3. Graph: y = 1.5sin (4x + 4/3π) + 0.5
amplitude = 1.5
period = π/2
phase shift = π/3
'y' shift = 0.5
b=4
An example:

4. per = 2π
amp = 1
Sine and Cosine
The shape is the same as the sine wave but
displaced a distance of π ⁄ 2 to the left on the
horizontal axis. This is an example of a phase
shift.
amp = 1
per = 2n

5. I have learned that we need amplitude, period, and phase shift to determine
what kind of periodic wave is going to come out of the equation. I also
learned that there is a formula to find out the period, amplitude, and phase
shift. I am also aware that if its a positive them the periodic wave is going to
go to the left and that if its a negative then it goes to the right.
My Understanding