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Theta


Date: 04/14/97 at 10:22:18
From: Cecil Allen
Subject: Theta

What is Theta?  Does it have a constant value?


Date: 04/14/97 at 12:39:44
From: Doctor Wilkinson
Subject: Re: Theta

The Greek letter theta is just used as a variable name, much like x 
and y.  For some reason it is most commonly used to denote an angle.  
But no, it doesn't have a constant value.

The most common use is as the angle coordinate in polar coordinates.  
That is, the point designated by (x, y) in so-called Cartesian 
coordinates (so-called after Rene Descartes, who invented them), is 
usually denoted by (r, theta) in polar coordinates.  That is, 
(r, theta) denotes the point whose distance from the origin is r and 
such that the angle between the positive x-axis and a ray drawn from 
the origin through the point is theta. 

The Cartesian and polar coordinates are related by the formuulas

   x = r cos(theta)
   y = r sin(theta).

In very advanced mathematics there are things called theta functions, 
but I think that's probably not what you were looking for.

I have tried to cover as many uses of theta as I could think of.  I 
hope I have succeeded in answering your question.

-Doctor Wilkinson,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
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