Re: Arctan: to use with single or with double arguments?

[Adam Beneschan <adam@irvine.com>]

On Feb 10, 4:26 pm, Jack Mitchell <j...@home9999.plus.com> wrote:
> Am I missing something - surely :-
>
>         z = Force * SIN(ATAN2(x,y))
>
> Is the same as :-
>
>         z = Force * x / sqrt( x^2 + y^2 )
>
> This should be much faster (and probably more accurate)
> Perhaps I have got x & y swapped but you see my point.

Yep, the arguments to Arctan in Ada (and I believe the arguments to
ATAN2 in Fortran) are
(Y, X).  So what you should have said (since this is an Ada newsgroup)
is

   z := Force * Sin(Arctan(Y, X));

is the same as

   z := Force * Y / Sqrt (X**2 + Y**2);

I did have to rewrite this so that I wouldn't go nuts trying to switch
the X and Y axes on a diagram.  But it appears that you're right.  The
sign is correct, i.e. Sin(Arctan(Y, X)) is negative when Y is negative
and positive when Y is positive.  Similarly, Cos(Arctan(Y,X)) is the
same as X / Sqrt (X**2 + Y**2).

                         -- Adam