Section 4.5 – Writing Equations of Sine and Cosine Graphs
Objective – Given the characteristics of the graph, write the equation of the sine or cosine curve.
Now we are working backwards.
Example: Sine graph, amplitude = 4, period =
Equation:
Cosine Graph, amplitude = 1, reflect over x-axis, phase
shift
4
, frequency = 1
Cosine Graph, amplitude = 2, phase shift
,
frequency = 1, up 4
Sine Graph, amplitude = 5, reflect over x-axis,
period =
2
3
, down 2
Sine Graph, amplitude = 1, period =
4
, phase shift 3
Find 2 equations for each graph. One using sine and one using cosine.
More Practice With Graphing – Sketch each over one period. Label all important values on the x
and y axes!
1.
2.
2cos4yx
3.
1
sin 2
2
yx
4.
1
cos
22
yx




5.
cos 2yx
