# How to Graph Lemniscates

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Graphing lemniscates is a process that will require you to examine the analytic equation. Graph lemniscates with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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## Video Transcript

Hello, my name is Walter Unglaub and this is how to graph lemniscates. So lemniscate is generally described by the analytic equation R squared is equal to A squared x sine of 2 theta or alternatively A squared times cosine of 2 theta, where A is not allowed to be 0 and this 2 indicates a frequency of two when you go from 0 to 2 Pi radians. So as an example, we can consider the lemniscate R squared is equal to 4 x sine of 2 T where T will range from 0 to 2 Pi radians or rads for short and when we solve this equation for R, we get + - because of the even power, the square root of 4 x sine of 2 T and this is going to be equal to + - 2 x the square root of sine 2 T and it turns out that either solution is equally valid provided that you go from 0 to 2 Pi in the argument of the sine. So what this looks like is going to be something like this there's two petals in this case and you flow along the trajectory as you increase the angle for at least one period and this is an example of a lemniscate. My name is Walter Unglaub and this is how to graph lemniscates.

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