Monday 1 June 2020

Amplitude, Period, Phase Shift, Vertical Shift, and Frequency


Some functions (like sine and cosine) repeat forever and are called Periodic Functions.

Amplitude
  • It is the height from the center line to the peak (or to the trough). Or we can measure the height from highest to lowest points and divide that by 2.
Period
  • It goes from one peak to the next (or from any point to the next matching point).

Phase Shift
  • It is how far the function is shifted horizontally from the usual position.

Vertical Shift
  • It is how far the function is shifted vertically from the usual position.

Frequency
  • It is how often something happens per unit of time (per "1").
General Equation:

\begin{equation} y = A sin ( B x \pm C ) \pm D \end{equation}
\begin{equation} P = \frac{2\pi}{B} \end{equation}
\begin{equation} F = \frac{1}{P} \end{equation}

Where:
A = Amplitude
C = Phase Shift (when positive, it is shifted to the left; when negative, it is shifted to the right)
D = Vertical Shift (when positive, it is shifted upward; when negative, it is shifted downward)
P = Period
F = Frequency

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