Posted by **Jake** on Sunday, June 6, 2010 at 9:36pm.

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?

- trig -
**Reiny**, Sunday, June 6, 2010 at 9:48pm
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

- trig -
**MathMate**, Monday, June 7, 2010 at 7:57am
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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