Re: how to get the angle from the cosine, etc.
From: Peter Webb (webbfamily-diespamdie_at_optusnet.com.au)
Date: 10/03/04
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Date: Sun, 3 Oct 2004 21:05:10 +1000
"Sean Hunt" <seanstewarthunt@hotmail.com> wrote in message
news:22c674bb.0410022331.1ab5c3a4@posting.google.com...
> Adam,
>
> Thank you very much for the response!
>
> I'm actually looking for a way to get the angle (in radians), given
> that you already have the sine and cosine of the angle. I'm trying to
> derive an equation to go back and forth rather than a look-up process,
> so that the angle can be calculated as a result, and not approximated
> by finding a table value that comes close.
>
> On the surface it looks like a fairly easy correlation, but I
> haven't been able to calculate the angle given sine and cosine. Now
> I'm beginning to think that this might be a calculus problem rather
> than a trigenometry problem.
>
> Thanx...
> Sean
Just to elaborate a little ...
The function that does the opposite of sin is called asin or arcsin. Just as
sin is not equal to something simpler, like x^2-1, arcsin is also not equal
to something simpler.
If you have some means of calculating sin - like using a scientific
calculator, a programming language, Excel, etc - you almost certainly also
have the asin (or arcsin, or inverse sin) function in that environment.
On the unlikely chance that you don't, there is a general technique for
numerically calculating the inverse of a function, known as Newton Raphson.
(There are even better ways, but this one is so good and so simple that its
an excellent first choice.)
http://www.google.com.au/search?hl=en&ie=UTF-8&newwindow=1&q=newton+raphson&spell=1
If you want to find arcsin(0.25), just use Newton Raphson to solve
sin(x)=0.25.
Don't try it with numbers bigger than 1 (or less than -1) as these don't
have arcsin defined (in a form you could use), as all sines are between -1
and 1.
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