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Thread: Cyclic proof for trig

  1. #1
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    Cyclic proof for trig

    Please could someone suggest how do i prove that d^(2n)y/dx(2n) =(-1(^n))*sin(x)

    basically if you keep finding the first, second third etc. differential of sinx or cosx they always continue in a cycle how do i formally prove ty
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  2. #2
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    Re: Cyclic proof for trig

    I recommend Induction. Check out the Wikipedia article on how to word a proof by induction:

    https://en.wikipedia.org/wiki/Mathematical_induction
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  3. #3
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    Re: Cyclic proof for trig

    Quote Originally Posted by DiscreteMathHelp View Post
    Please could someone suggest how do i prove that d^(2n)y/dx(2n) =(-1(^n))*sin(x)
    basically if you keep finding the first, second third etc. differential of sinx or cosx they always continue in a cycle how do i formally prove ty
    I am no fan of proofs by induction for cyclic formulas
    $ \begin{align*}y&=\sin(x)\\y^{(1)}&=\cos(x)\\y^{(2) }&=-\sin(x)\\y^{(3)}&=-\cos(x)\\y^{(4)}&=\sin(x) \end{align*}$

    We now have a complete cycle.

    Suppose we want the $146^{th}$ derivative. Well $146=4(36)+2$ hence $y^{(146)}=-\sin(x)$
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