I know that for scientific calculators it would be a little redundant. However, for calculators that do symbolic manipulation (ie, TI-92) it would be a big help to have those functions built in. A function can be much, much clearer when it is not always “simplified” in terms of SIN, COS, and TAN.
you can probably redefine sec, cot, csc on a ti92, I know you can on a TI-89. They probably dont include it because of the limitted space.
Okay, first off, you know you can define sec(x) = 1/cos(x), right? But you want more. You want to be able to put in d(sec(x), x) and get back out sec(x) * tan(x), right? Right now, if you do it, you get sin(x) / (cos(x))[sup]2[/sup]. But really, I think it would be ambiguous. How would the calculator know that you want sec(x) * tan(x), and not sin(x) * (sec(x))[sup]2[/sup], and not sec(x) / cot(x)?
Hmmm… Good question.
Would it really be that hard to create an algorithm that would derive the simplest form of the equation?
No, but you have to say unambiguously what you mean by simplest form. I think that getting it in terms of sines and cosines is a reasonable definition of simplest form.