Definition of a TangentDate: 10/27/95 at 23:46:22 From: Anonymous Subject: What is a tangent of an angle? I am a senior and I have already taken Geometry, but for some reason I can't seem to remember what the tangent of an angle is. I have asked my parents and looked in a few encylopedias and dictionaries, but I haven't been able to find out which one it is. I wouldn't be asking, but I have an interview for a job tomorrow and the boss asked me what the tangent of an angle is. Q: What is the tangent of an angle? Thanks for your time I am sorry to have to bother you. Date: 10/28/95 at 11:35:6 From: Doctor Ken Subject: Re: What is a tangent of an angle? Hello! I hope this response reaches you in time. The tangent of an angle can be thought of in a couple of different ways, one of which is easy to think about, the other of which is a little more correct and a little more general. They're essentially the same thing, though. 1) If you're dealing with right-triangle trigonometry, then the tangent of an angle (not the right angle) is the ratio of the opposite side to the adjacent side. For instance, if you have a right triangle whose 3 sides have length 1, Sqrt{3}, and 2, the tangent of the angle opposite the side of length 1 is 1/Sqrt{3}. Look at the picture and justify that to yourself. By the way, the angle in question is 30 degrees. |\ | \ | \ 2 Sqrt{3} | \ | \ |_____\ 1 2) The somewhat more rigorous way. Tangent is actually defined in terms of Sine and Cosine. It's defined as Sine/Cosine. So then you have to ask "what are Sine and Cosine defined as?" Well, they're defined in terms of a circle of radius 1. Do the following: draw a circle of radius 1 that's centered at the origin of a coordinate system. Then draw a ray that starts at the origin and makes an angle b with the x axis (you go around counterclockwise from the x axis until you hit the ray). Cosine and Sine are the coordinates of where that point intersects the circle. Cosine is the x coordinate, and Sine is the y coordinate. So then once you have Sine and Cosine, you can divide them to get Tangent. -Doctor Ken, The Geometry Forum |
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