How to Do Trigonometry Sine Waves

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Performing trigonometry sine waves isn't nearly as complicated of a process as you might be assuming it is. Do trigonometry sine waves with help from a mathematics educator in this free video clip.

Part of the Video Series: Trigonometry Education
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Video Transcript

Hi, I'm Jimmy Chang and we're here to talk about how to do trigonometry sine waves. Now as you might imagine if you've studied the sine function by now you'll now that the sine function graph is that of a wave. So in terms of how to do the trigonometry sine wave, you want to just think about creating an X Y chart using the function Y is equal to sine of X and so let's look at a quick X Y chart and you'll kind of see how all of this goes. Now being that we're using angles here, let's start off with the most common angles that we know about when it comes to sine and that will help you draw it pretty easily. It always is nice to start out with the angle 0 and then Pi over 2, Pi, 3 Pi over 2 and then 2 Pi, just to kind of close out the cycle if you will. Now what you're going to do is you're going to plug in all of these individually in place of X and you'll go from there. Now when you plug in 0 sine of 0 is equal to 0 so when X is 0, Y is 0. Now for Pi over 2, sine of Pi over 2 is equal to 1, that's one of those common trig values. Now with Pi, sine of Pi is 0, for 3 Pi over 2, when you plug that in place of X, sine of 3 Pi over 2 is equal to negative 1. So Y is negative 1 and then 2 Pi, now 2 Pi, you've come full circle so 2 Pi is going to have the same value on the Y side as 0 so Y is going to be 0. Now in terms of plotting it, think about it this way, make ticks for Pi over 2, Pi, 3 Pi over 2 and 2 Pi. Now keep in mind that the sine waves as well as cosine waves, they keep on going. So this just represents one sample of it. So when X is 0, Y is 0, Pi over 2, 1, Pi 0, 3 Pi over 2 is going to be right here and then 2 Pi is like this. So the idea here is just, and this would be a rough sketch, a wave goes like this. Now the graph does continue so let me just draw it going this way to kind of show you that the graph does continue. But I would definitely keep in mind that this is the pattern of a sine wave because you are going to be using it for other sections in trigonometry as well as other math courses. So I'm Jimmy Chang and this is the process on how to do trigonometry sine waves.


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