Is there a general way to find a numeric approximation of the sine or
cosine of an angle(eg. sin53) without using a calculator or table? I
would like to know this process for use beyond the typical (45*, 30*,
60*, 90*, etc.) angles. Just a link to a page describing the process
would be fine. Thanks!

losvedir-ga,

Thanks for the opportunity to answer your question!

I found a page that discussed this very topic at:

http://mathforum.org/library/drmath/view/53964.html

An excerpt:

"But I gather that you're looking for a more algebraic, formulaic way?  Well,
there's no algebraic way to compute exactly the trigonometric values of 
every angle, only certain ones like Pi/2, Pi/3, Pi/4, and things like that.
You can, however, use an algebraic formula to find an _approximation_ to 
any angle.  To approximate Sine, use the formula 
     x^3      x^5       x^7
x - ----  +  -----  -  ----- + ....
     3!        5!        7! 

For cosine, use the formula

     x^2      x^4       x^6
1 - ----  +  -----  -  ----- + ....
     2!        4!        6! 

These both converge pretty quickly to the right value, and they converge 
most quickly when x isn't too far away from 0."

Best regards!
arimathea-ga
Researcher

Research strategy:  find sine cosine angle "without table" search on Google.

Thank you! That was exactly what I was looking for!