Contact The Learning Centre

# 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 $$-1$$