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Q: Solving sine and cosine without a calculator or table. ( Answered 5 out of 5 stars,   0 Comments )
Subject: Solving sine and cosine without a calculator or table.
Category: Science > Math
Asked by: losvedir-ga
List Price: $10.00
Posted: 27 Jun 2003 17:47 PDT
Expires: 27 Jul 2003 17:47 PDT
Question ID: 222630
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!
Subject: Re: Solving sine and cosine without a calculator or table.
Answered By: arimathea-ga on 27 Jun 2003 17:56 PDT
Rated:5 out of 5 stars

Thanks for the opportunity to answer your question!

I found a page that discussed this very topic at:

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!

Research strategy:  find sine cosine angle "without table" search on Google.
losvedir-ga rated this answer:5 out of 5 stars
Thank you! That was exactly what I was looking for!

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