How to Figure Out the Period Given With a Trig Graph

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Figuring out the period given with a trig graph is something you can do by graphing the function in question. Figure out the period given with a trig graph 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 figure out the period given with a trig graph. So, here I have my Y, T plane where Y is a function of time and let's say I have a trigonometric graph, in this case a sinusoid where the amplitude is equal to A, so I have positive A here, negative A here. I notice that the sine, 0 at Pi but then returns to 0 at 2 Pi and if I were to continue the T axis I would have repetitive behavior. So I can write down a function for this, in this case it would be A x sine of T. But it turns out that generally I can have a frequency Omega T inside of the sinusoid. And if this frequency is higher then my period will be smaller. So, the period then is defined as the change in time over which the signal or in this case this function repeats and so all I would have to do is calculate the period by subtracting from the final time the initial time. So in this case, I would have 2 Pi minus 0 which is just equal to 2 Pi in whatever units of time my X axis is in. Generally, however, the angular frequency Omega is equal to 2 Pi F. This is the equation that relates linear frequency to angular frequency and linear frequency is simply 1 over the period, therefore, whatever number appears in front of the independent variable in the sinusoid is going to be your Omega and that's going to be equal to 2 Pi F or 2 Pi divided T. Therefore, the period is going to be equal to 2 Pi divided Omega. We see that in our simple example. My Omega is going to be equal to 1 because this is just a 1 being multiplied to the T, therefore, 4 Omega is equal to 1, my period is 2 Pi as I confirmed by simply looking at my graph of a trigonometric function. So this is how you find the period for a given trigonometric function that exhibits periodic behavior. My name is Walter Unglaub and this is how to figure out the period given with a trig graph.

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