Advanced Math-Honors
Graphing Sine and Cosine
General Graphs
• Graphs are collections of points
• Independent variables are related to
dependent variables
• Domain is set of independent variable
values
• Range is set of dependent variable values
Periodic Graphs
• Graphs that repeat infinitely in intervals
are called periodic
• Ex: Sea level as a function of time
• The most common periodic graphs are the
graphs of the trigonometric functions
• Sine, cosine, tangent, cosecant, secant, and
cotangent
The Sine Graph
 2

3
2



2
0

2

3
2
2
Oscillation-one complete “cycle” of the graph
Period-”time” (horizontal distance) it takes the graph to complete one oscillation
Amplitude-the furthest vertical distance the graph ventures from the vertical center
The Sine Graph
 2

3
2



2
0

2

3
2
•We think of the sine graph as starting at an x-value of zero
•It begins at a y-value of zero
•It then moves up the distance of its amplitude
•Next it moves back down to the x-axis
•Then it moves down the distance of its amplitude
•The it completes an oscillation by moving back up the x-axis
2
The Sine Graph
 2

3
2



2
0

2

3
2
2
•The period of the sine graph is…
•So the horizontal length of each “piece” of the sine graph is…
•The amplitude of the sine graph is…(think about the values of sine)
The Cosine Graph
• The cosine graph is the same as the sine
graph, only it has been shifted horizontally
• Same period
• Same amplitude
The Cosine Graph
 2

3
2



2
0

2

3
2
2
•Same period
•Same amplitude
•The “starting point” is still an x-value of zero, but is now a y-value of 1
Sine and Cosine Graphs
• While the idea of a “starting point” is very
helpful when graphing, it is merely an idea
• These graphs have infinite domains
• We have thus far only looked at library
versions. There will be transformations.