Graphing Sine and Cosine www assignmentpoint com General

General Graphs • Graphs are collections of points • Independent variables are related to

Periodic Graphs • Graphs that repeat infinitely in intervals are called periodic • Ex:

The Sine Graph Oscillation-one complete “cycle” of the graph Period-”time” (horizontal distance) it takes

The Sine Graph • We think of the sine graph as starting at an

The Sine Graph • The period of the sine graph is… • So the

The Cosine Graph • The cosine graph is the same as the sine graph,

The Cosine Graph • Same period • Same amplitude • The “starting point” is

Sine and Cosine Graphs • While the idea of a “starting point” is very

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Graphing Sine and Cosine www. assignmentpoint. com

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 www. assignmentpoint. com

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, and cotangent www. assignmentpoint. com

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 www. assignmentpoint. com

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 www. assignmentpoint. com • The it completes an oscillation by moving back up the x-axis

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) www. assignmentpoint. com

The Cosine Graph • The cosine graph is the same as the sine graph, only it has been shifted horizontally • Same period • Same amplitude www. assignmentpoint. com

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 www. assignmentpoint. com

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. www. assignmentpoint. com