trig
posted by Jake .
Regarding the trigonometric series,
Why does cos start with a 1 and why are the powers of x even numbers
Also for sin, why does sin start with an x and why are the powers odd?

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/Seriesexpansion/2_Maclaurinseries.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?