How to Find the Period of a Graph


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 y-value of the graph. Look for a peak in the graph’s height. Note the x-coordinate at which a peak y-value occurs.

  • Move right along the x-axis of the graph. Locate the next peak y-value. Record the x-coordinate at which the second peak y-value occurs.

  • Subtract the x-coordinate for the first peak y-value from the x-coordinate for the second peak y-value. Write down the difference between the two x-coordinates. That difference is the period of the graph.


  • Photo Credit Comstock/Comstock/Getty Images
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