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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
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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
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The Sine Graph
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
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The Sine Graph
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
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Page 6 of 9
The Sine Graph
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)
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Page 7 of 9
The Cosine Graph
The cosine graph is the same as the sine graph, only it has been shifted horizontally
Same period
Same amplitude
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Page 8 of 9
The Cosine Graph
Same period
Same amplitude
The “starting point” is still an x-value of zero, but is now a y-value of 1
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