Re: how to get the angle from the cosine, etc.
From: Adam (addam_at_rogers.com)
Date: 10/03/04
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Date: Sun, 3 Oct 2004 11:11:47 -0400
"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.
>
If you know the sine, then you also know the cosine. To me, the cosine
is just the sine function translated by 90 degrees or PI/2 radians. The
website I gave a link for shows how this was developed. You may be looking
for a simple equation where you can either solve for the angle or solve for
the sine of the angle by algebraically manipulating a single equation. I
don't think that can be done, but I'm far from a math expert. The problem is
that the sine is non-linear, and even its expansions will be non-linear.
Suppose you were to ask me to fine the sine of a given angle, and
stipulated that I wasn't to use any devices to solve for it (like arcsin on
calculators). I would most likely use the old method to find the sine for
any integer angle, and then interpolate to find a non-integer angle. It
would basically be creating a look-up table for sine. I would just use it in
reverse to fine the angle given the sine; just like people did in days of
old. I don't have the experience to figure it out any other way.
Trigonometry was arbitrary. So you have to go along with conventions.
> 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.
It might be easier if you had other constraints to use. Like the angle
belonging to a right-angle triangle.
Good luck, Adam.
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