Sine and Cosine Graphs

Amplitude: is half the distance between the maximum and minimum on the graph. (height of one wave)

- Amplitude = |a|

Period: the length from one crest to the next (wavelength)

- 2π/b

Translations: y= a x sin (b (θ - c)) + d

• Y creates a vertical change

• A creates a vertical change. The larger the number, the longer the stretch becomes

• B creates a horizontal change. The larger the number, the more compressed the graph becomes.

• θ creates a horizontal change

• C creates a horizontal change. It shifts to the left if positive, and the right when negative.

• D causes the entire function to shift up or down Y creates a vertical change

Phase Shift: Sin(θ + 2π) = Cos

Sine Graph:

• Crosses through the origin
• Amplitude is 1
• Period is 2π

Cosine Graph:

• Starts at 1
• Amplitude is 1
• Period is 2π