Components of Trigonometric Graphs

The amplitude, \(a\),  describes the distance from the midline, which can be computed by taking the average of the maximum and the minimum. 

\(\displaystyle\text{amplitude}=\,\frac{\text{max}+\text{min}}{2}\)

The periodicity describes the length \(p\) of function before it repeats, and starts a new cycle.

The frequency, \(\omega \), describes how often something occurs over a given unit of time. 

\(\text{frequency} = b \)

The phase shift describes the horizonal shift from the base graph. 

\(\displaystyle \text{phase shift}=\frac{-c}{b} \)

The midline, \(d\), is the horizontal line of symmetry, which describes a vertical phase shift.  

\(\displaystyle\text{midline} =\, \frac{\text{max}-\text{min}}{2} \)