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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 -

    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

  • trig -

    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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