Posted by Jake on Sunday, June 6, 2010 at 9:36pm.
You must be referring to the expansion so sinx and cosx
sinx = x - x^3/3! + x^5/5! - x^7/7! + ... and
cosx = 1 - x^2/2! + x^4/4! - x^6/6! ...
I don't know if you have learned about the Taylor Series expansion.
Here is a page that develops the sinx expansion
http://www.intmath.com/Series-expansion/2_Maclaurin-series.php
The above reference should help you to answer the questions:
Why does cos start with a 1 and why are the powers of x even numbers
- think of what cos(0) equals, and
- is cos(x) an even or odd function?
Also for sin, why does sin start with an x and why are the powers odd?
- Evaluate lim sin(x)/x as x->0
- Is sin(x) an even or odd function?
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