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Math Help - different answers for derivative?

  1. #1
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    Question different answers for derivative?(Solved)

    Take this trigonometric function:

    \frac{d \(sin{(\cos{\theta})})^2}{d \theta}}

    Using the chain rule i think it becomes:

    -2\theta\sin{(\cos{\theta})}\sin{\theta}

    But if we use the identity:

    \sin^2{\theta} = 1-\cos^2{\theta}

    then the equation becomes

    \frac{d  (1-\theta^2)}{d \theta}} = -2\theta

    But if,

    -2\theta = -2\theta\sin{(\cos{\theta})}\sin{\theta}

    then,

     \sin{(\cos{\theta})}\sin{\theta} = 1

    Which doesn't appear so. Why am I getting different answers for the same derivative? Did I do something wrong in the above steps?


    I accidentally took :

    \cos(\cos\theta) = \theta

    P.S. This is my first post and using [tex] is VERY slow and irritating, is there a faster way to insert math expressions
    Last edited by dhtikna; March 1st 2013 at 06:44 AM. Reason: Correcting a mistake
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  2. #2
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    Re: different answers for derivative?

    Quote Originally Posted by dhtikna View Post
    Take this trigonometric function:
    \frac{d \(sin{(\cos{\theta})})^2}{d \theta}}

    Using the chain rule i think it becomes:
    -2\theta\sin{(\cos{\theta})}\sin{\theta}

    This part of the post is correct. But none of the rest makes any sense.

    It is the case that \sin^2(\cos(\theta))=1-\cos^2(\cos(\theta)). But that cannot be simplified.

    They both have the same derivative.
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  3. #3
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    Re: different answers for derivative?

    cos(arccos(x))= x but you have cos(cos(\theta)) which is NOT \theta.
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    Re: different answers for derivative?

    I Can't belive i was so stupid. I hadn't been doing trig for a long time so i messed up when I took:

    \cos({\cos\theta}) = \theta

    By the way, any have a answer to my P.S.:

    P.S. This is my first post and using [tex] is VERY slow and irritating, is there a faster way to insert math expressions
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  5. #5
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    Re: different answers for derivative?

    Quote Originally Posted by dhtikna View Post
    I Can't belive i was so stupid. I hadn't been doing trig for a long time so i messed up when I took:

    \cos({\cos\theta}) = \theta

    By the way, any have a answer to my P.S.:

    P.S. This is my first post and using [tex] is VERY slow and irritating, is there a faster way to insert math expressions
    Yes, get good at copying and pasting the preamble, learn the code and type faster :P
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