[Gllug] Light the blue touchpaper...

[Chris Bell]

On Thu 18 Mar, Pete Ryland wrote:
> 
> On Wed, Mar 17, 2004 at 06:58:29PM +0000, Chris Bell wrote:
> >    Calculating tan x on paper is not very easy without knowing what you are
> > doing. I was taught using a combination of graphical/geometrical methods,
> > calculus, complex numbers, and all depending on my current understanding of
> > the theory behind the different methods at the time. Teaching and
> > understanding the trig functions using geometrical methods does not rely on
> > understanding complex numbers, but complex number theory can help understand
> > and calculate both trig and hyperbolic functions quickly and easily once
> > complex numbers are understood.
> 
> Interesting... I agree that complex numbers and trig are certainly very
> relevant to each other, but how does an understanding of complex numbers
> help you calculate tan(0.34) for example?
> 
> Pete

   I am afraid that it is a very long time since I was shown how all of the
trig and hyperbolic functions can be generated using complex numbers, but it
relied on the ways that component terms cancelled when using simple simple
squares and square roots of complex numbers, and it is not difficult to
calculate squares and square roots accurately by hand. I am sure there are
other ways as well, (but not that I can remember at this time of night.)

-- 
Chris Bell

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