How to Graph Sine Functions With Fractions

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Graphing sine functions with fractions is easy, so long as you know which steps you have to follow. Graph sine functions with fractions with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: College Math
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Video Transcript

Hi, I'm Jimmy Chang and we're here to talk about how to graph sine functions with fractions. Now, if you've been working in Trigonometry for awhile, you'll know that oftentimes Trigonometry uses a lot of fractions especially when it comes to radian form because radians when you express them angles in that way are often in fraction forms. So, when it comes to sine, it's very similar. So, first and foremost, we're going to create and XY chart of the sine function. Y equals sine of theta and we're going to use radians to illustrate our point. And we're going to do zero, pie over two, pie, three pie over two and two pie. Now, when you're going to plug in every single one of these and remember x can be thought of as theta if you like and so, sine of zero is going to be zero, sine of pie over two is going to be one, sine of pie is going to be zero, sine of three pie over two is going to be negative one and sine of two pie is going to have the same value as zero which is going to be zero. Now, when it comes to graphing it, the idea works like this. What we're going to do is mark these, label these and this gives you one cycle of the sine function. So, zero, zero; pie over two one is going to be like so, pie zero is going to be like this, three pie over two negative one is going to be just, I would say roughly about here and then two pie is going to be zero. And then you're just going to graph like this; but understand of course that the graph does continue. So, sometimes people will extend the graph using data lines to show that the graph does continue, doesn't actually end. So, as long as you follow this particular strategy and understand that radians oftentimes imply fractions, you should be fine. So, I'm Jimmy Chang and that's how to graph sine functions with fractions.


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