[TI-M] Re: disable hyperbolic
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[TI-M] Re: disable hyperbolic
> when i type (e^x-e^(-x))^2
>
> i get the answer in terms of hyperbolic trig functions 4 (sinh(x))^2
> is there a way to disable this feature as to get responces in terms of e?
Well, this one you might as well do by hand. . .
(a-b)^2 is a^2-2ab+b^2
so (e^x-e^(-x))^2 = e^2x - 2(e^x)(e^-x) + e^-2x = e^2x + e^-2x - 2
but if you still insist on using the calc, try using some of these:
expand(4sinh(x)^2) = (e^x)^2 + 1/(e^x)^2 - 2
which is the same thing, although you'll note that (e^x)^2 then isn't
simplified to e^2x
interestingly, if you enter that in the command line, it'll simplify to
2cosh(2x)-2, which happens to be equivalent to 4sinh(x)^2
another way to do it:
tExpand(4sinh(x)^2) = (e^-2x)(e^(4x)-2e^(2x)+1)
which you can simplify yourself to e^(2x)- 2 + e^(-2x), which is again
equivalent to the above answers.
So there's still no magic bullet, unless TI writes a CAS that will do these
things step-by-step for you (not likely). The HP49 will solve things
step-by-step, but with a completely different CAS you could encounter all
kinds of different quirks. I don't have one to try myself.
A calculator by itself won't solve problems for you as you get into higher
math. Back in calc 2 and 3 this was especially true -- the calculator's
answers to some complex integrals are baffling. But if you have a good
knowledge of what's going on, you can often convert those answers into
similar ones that makes sense or give you a hint on what direction to take
yourself. Even when the answer makes even less sense, you can compare it
with your own answer by plugging in some values and seeing if they're
equivalent.
-Scott