A Simple Trigonometry question about Cosines

A Simple Trigonometry question about Cosines

Postby Xarzu » Mon Sep 25, 2017 7:36 pm

This is a very simple question I am sure for anyone who works with mathematics or is currently studying mathematics. Unfortunately, I have not touched this stuff in decades and I am a bit rusty.

How do I determine what an angle is on an X and Y grid of a line that intersects a circle drawn on that grid (both the line and the circle are centered at (0,0) )? If we know that point at which the line intersects the circle, how can that be converted into a degreed angle?

Here is another way of asking the same question. If I have an X and Y point on a grid that represents the intersection of two formulas:  A straight line (aX = Y) where "a" represents a constant number with a circle [tex]x^{2}[/tex] + [tex]y^{2}[/tex] = [tex]radius^{2}[/tex], how would I convert that point into a degree of an angle? The angle would represent the line function albeit only go one direction on the grid. It would be some degree.

If I were to guess, this might be very simple and have something to do with cosine rules.

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Re: A Simple Trigonometry question about Cosines

Postby Guest » Thu Oct 05, 2017 1:19 pm

If I understand your question (and I think I do if I make a few obvious assumptions) then getting the angle is quite simple. Since you know the x-coordinate and the y-coordinate of the point where the line intersects the circle (there will actually be 2 points of intersection but I assume you are interested in the point of intersection in either quadrant I or quadrant IV) use the fact that the tangent of an angle is opposite / adjacent. Since the circle is centered at the origin and the line goes through the origin, your value for opposite is the y-coordinate and your value for adjacent is the x-coordinate. Now use the tan inverse (or arctan) function to go from the value of the tangent to the angle.


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