# Graphing of Trigonometric Functions

### Trigonometric graphs

The graph of \(y = A \sin [B(x - C)] + D\) is determined by four numbers, \(A\), \(B\), \(C\) and \(D\)

- \(A\), the amplitude, tells the height of each peak and the depth of each trough
- \(B\), the frequency, tells the number of full patterns that are completed in a space of \(2\pi\)
- The period of the function is \(\displaystyle \frac{2\pi}{B}\)
- \(C\), the phase shift, is horizontal movement from the origin
- \(D\), the offset, is the vertical movement from the origin

For example, the graph of \(y = 3 \sin (2x) - 1\) will look like:

- the amplitude, height of each peak is \(3\)
- the frequency, number of full patterns in a space of \(2\pi\) is \(2\)
- The period is \(\displaystyle \frac{2\pi}{2}\) or \(\pi\)
- the phase shift is \(0\)
- the offset is \(-1\)