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Trig functions challenged

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6 February 2008



LUDDITE, Kentucky -- In a stunning about-face from their previous position, pre-calculus teachers across the world have suddenly decided that circles are not the simplest conic sections.

"It's really incredible that we never noticed this until now," said one.

Apparently, the teachers have determined that the trigonometry supporters' claims that trig functions are simpler than the hyperbolic functions are complete rubbish. They cited several impressive examples to back up their assertions:

  1. The hyperbolic functions aren't periodic. As another teacher put it, "No more messing with restricted domains and all that crap."
  2. The hyperbolic functions have simpler definitions. For example, the definition of sinh(x) is \frac{e^{x} - e^{-x}}{2}, while the definition of sin(x) is \frac{e^{ix} - e^{-ix}}{2i}. Obviously it is much easier to remember the first one.
  3. The hyperbolic functions are easier to differentiate. \frac{d}{dx}(cos(x)) = -sin(x), but \frac{d}{dx}(cosh(x)) = sinh(x).

In response, conservative pro-trig nuts have demanded that the old teachings be continued, or at least taught alongside the new functions. One person responded by sending a letter advising state officials that he is a member of the Flying Hypergeometric Function religion curriculum and requesting that such functions should be taught alongside both the hyperbolic functions and the traditional trigonometric functions.

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