Cosine Graphs

How to Graph a Cosine Graph

A Cosine graph has a parent equation of y=a cos bx.

"a" dictates the amplitude. The distance between a peak (or trough) and the mid-line. Also known as half the distance between "peak" and "trough" on the graph. A negative a reflects the graph "upside down".

"b" is the number you will use to find the period and frequency of your graph. To find period set up the equation p=2π/b with "p" being your period. When making the graph the Period is how long it takes the function to complete 1 full cycle. So from the maximum to the center to the minimum, then back up to the center then the maximum.

Once you find the period you need to find the intervals to put your "key points" on your graph. Take the number you found for your period and divide it by 4. That is how much you will go over by until you get to the period number.

Key points are the points that show the minimum, maximum, and center points of your graph. when making a cosine graph your first point is at (0,amplitude) then you go to center line, down to the minimum, then back to the center line, and then back to the maximum. At this point you should be to the period number of your graph and have 1 complete cycle elapsed.   


Below is an example of a cosine graph with an amplitude of 1 and a period of 2π. This is the parent graph of a cosine function.