Writing Trig Functions in x-Base

Date: 24 May 95 21:40:06      
From: Anonymous
Subject: Writing Trig Functions in x-Base
 
I must write trig functions (sin(), cos(), etc) in xBase code as part of 
a project that I am working on (navigation bearing and distance 
calculations).  I am aware that dBase itself includes trig functions, 
but for this project I must use a specific xBase implementation which 
doesn't include the necessary functions.  Could you recommend 
any good reference books for this?  An algorithmic approach would 
be preferred as it would be easier to convert into actual programming 
code.  However, a mathematical approach would be acceptable too.  

Of course, if this request is considered trivial enough, please feel free 
to provide actual algorithms instead.  Any assistance would be very 
much appreciated.  Thank you.

Andy Cornell, acorne1@ibm.net

Date: 9 Jun 1995 10:53:11 -0400
From: Dr. Ken
Subject: Writing Trig Functions in x-Base

Hello there!

I'm sorry it has taken us so long to get back to you on this.  I don't know
a whole lot about xBase, but if I were you, I'd probably be inclined to try
the Taylor expansion for the trig functions, as long as the angles you're
going to plug in to the functions don't get too far from your basepoint.

For instance, if your angle is pretty close to zero, you could have your
program use the approximation x - x^3/6 + x^5/120 for Sine.  The
approximation will stop being very good once you get outside the interval
(-Pi/8, Pi/8), so outside that you'd probably want to use the Taylor
expansion around a different base point like Pi/4 or something.  

You can do the same thing for Cosine, and then you can write the remaining 
trig functions in terms of Sin and Cosine, or you can use the Taylor 
expansions of the other functions.  If efficiency and accuracy are important 
in your program, you'll probably want to use the Taylor expansion of 
each function rather than writing everything in terms of Sine and Cosine.

If you need more help in actually figuring out the Taylor expansions, let us
know.

-K