Certain trigonometric functions, such as sine or cosine functions, have graphs that fluctuate back and forth in regular intervals. The shortest interval at which the shape of a graph repeats itself is called the period of the graph. While students can determine the period mathematically using the trigonometric properties of functions, they can also learn about the properties of a function by analyzing graphs of various functions. Learning how to find the period of a graph helps students visualize the tendencies of trigonometric functions.
Things You'll Need
 Graphing calculator or graph paper

Plot the function on a graphing calculator, or sketch it out on graph paper. On the calculator, change the window viewing settings so that you can see the pattern repeat at least once.

Find the maximum yvalue of the graph. Look for a peak in the graph’s height. Note the xcoordinate at which a peak yvalue occurs.

Move right along the xaxis of the graph. Locate the next peak yvalue. Record the xcoordinate at which the second peak yvalue occurs.

Subtract the xcoordinate for the first peak yvalue from the xcoordinate for the second peak yvalue. Write down the difference between the two xcoordinates. That difference is the period of the graph.
References
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