How to Find X & Y on Special Segments

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Finding X and Y on special segments will require you to place them on the X and Y planes. Find the X and Y on special segments 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 find x and y on special segments. So here I have a circle of radius r and I have a special segment which is essentially just this chord that I've placed on the x y plane where it meets up with the circle at this point and crosses through at some angle theta and leaves the circle at this point. So there are two commonly shared points between the special segment and the circle and what we're interested in is trying to relate to the two equations. So from the circle of course we'll have x squared plus y squared is equal to r squared where r is some primiter and some constant and x and y are variables. And for the line we can write the slope intercept form which is y is equal to mx plus b. So if we knew this height h for example and this distance, let's call it a, then we could calculate what the slope is. So m would be equal to the change in y divided the change in x and would simply be h over r plus a and this would be equivalent to tangent of the angle theta. So if we know the slope then we know one of the data points we can actually calculate what this y intercept denoted b would b. So what we have then is if this is true, then we have delta y is equal to m times delta x. The change in x would actually be r, the radius, so this delta y, the change in height would simply be m times r. So therefore we could simplify this in to mx plus mr and we would get y is equal to m times x plus r. And this equation would relate x and y, given a slope m which one could calculate given some other parameters and it would be dependent on the radius r of the circle. So given one point you can find another point along the line. My name is Walter Unglaub and this is how to find x and y on special segments.

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