How to Graph Radians

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When graphing radians, one factor you are going to have to consider is the unit circle. Graph radians 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 radians. Radian is a unit of measure for angles. So, if I consider the unit circle here, which is a circle of radius one. I can consider the angle that would additionally be required to specify a point on the circle, if I'm using polar coordinates. So, I can understand that the relationship between degrees degrees and radians by using the conversion factor, Pie over 180 degrees. So, if I have for example, 90 degrees, I can convert that to radians, if I multiply by my conversion factor. And this is simply going to be equal to Pie divided two radians or rads for short. So, going back to the example of the unit circle, if I wanted to look at a point along the circle as I plot it as a function of increasing angle. I can consider the range from zero degrees to 360 degrees. In radians, this translates to zero radians to two Pie radians using my conversion factor over here. And I notice, I'll start at one, if I'm looking at the X value. So, this will be F sub X of theta. And as I move along the radial and angular direction here, I go from one down to zero at 90 degrees or Pie over two radians. So, I'll be moving down sinusoidally to zero at Pie over two. And then, I go in the negative direction, back up to zero at three Pie over two, which is this. And then, finally back up to positive one at two Pie. Where this is actually negative one. So, this is a plot essentially of cosine of theta and the units are in radians. My name is Walter Unglaub, and this is how to graph radians.


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