Cotangent, Secant, Cosecant?!!

Jun 24, 2009 00:30

Has anyone run into the Cotangent or Secant or Cosecant functions since learning them in High School? Does anyone use them for anything? I do seem to remember a few mentions from calculus that fussed about secants, but why do we have special names for these things ( Read more... )

mathematics, request, teaching & studenting

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Comments 7

eeekster June 24 2009, 08:34:12 UTC
Since high school? We used them quite a bit in physics classes IIRC.

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wcg June 24 2009, 10:36:52 UTC
The most useful thing about these odd trig functions for me has been in solving weird integrals. If you have some strange thing that you can rearrange into the form of a trig function, you can then look its integral up in a table of standard integers.

I'm told they also have applications in electrical engineering, but I can't say I've ever seen that use directly.

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goodheartduck June 24 2009, 11:19:51 UTC
The comment about from wcg caused a few distant memory cells to light up, but other than that, I really can't remember any use for those reciprocal trig functions in my classes or my research. (I'm a chemical engineer by training.)

Strangely enough, the hyperbolic functions were used a lot in my graduate transport class, usually when solving second-order differential equations.

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nolly June 24 2009, 21:35:40 UTC
Yes; I was helping a coworker with a side project, and I used at least one of those. The project is a wiki-driven site showing the route traveled by the main character in each of a series of fantasy novels. He'd added arrow-flares to the lines to show direction of travel, but they were approximate, and didn't look quite right. I used at least one of those in calculating the correct angles for the arrow flares, so that they were always 45 degrees off the line, regardless of the line's angle. I think it was cotangent, but I don't currently have access to the source code to check.

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hitchhiker June 24 2009, 22:26:40 UTC
will ask on maths reddit :)

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hitchhiker June 24 2009, 23:06:48 UTC
http://www.reddit.com/r/math/comments/8vdid/ask_mathit_uses_of_the_reciprocal_trig_functions/

one very nice example already:

By the geometry of their construction, cylindrical projections stretch distances east-west. The amount of stretch is the same at any chosen latitude on all cylindrical projections, and is given by the secant of the latitude as a multiple of the equator's scale.

http://en.wikipedia.org/wiki/Map_projection

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