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Math Help - differentiation with trig functions

  1. #1
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    differentiation with trig functions

    Hi, I finally sorted the following table out and filed in the values,



    Now I have to find DT/DX (the rate of change of temperature) when X is equal to 150.

    I've only really touched on differentiation, if anyone could talk me through this example you'd really be helpng me out.

    Thanks.
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  2. #2
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    Quote Originally Posted by bobbymellor View Post
    Hi, I finally sorted the following table out and filed in the values,



    Now I have to find DT/DX (the rate of change of temperature) when X is equal to 150.

    I've only really touched on differentiation, if anyone could talk me through this example you'd really be helpng me out.

    Thanks.
    10\sin{\frac{2\pi x}{365}} + 25

    You need to use the chain rule on \frac{2\pi x}{365}

    f'(x) = 10cos(\frac{2\pi x}{365}) \times \frac{2\pi}{365} = \frac{20\pi }{365} cos(\frac{2\pi x}{365})

    f'(150) = \frac{20\pi }{365} cos(\frac{2\pi \times 150}{365})
    Last edited by e^(i*pi); April 14th 2009 at 09:16 AM. Reason: adding final answer
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  3. #3
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    Hey, thanks for the quick reply. Is that an acceptable solution to this example, or will i need to continue to solve the last part, f'(150)= ......
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by bobbymellor View Post
    Hey, thanks for the quick reply. Is that an acceptable solution to this example, or will i need to continue to solve the last part, f'(150)= ......
    You'll need to solve f'(150), I don't have a calculator near me so I can't reduce it to terms of pi or a decimal approximation
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  5. #5
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    ok thanks, would i be right in saying the rate of change for x = 150 is

    62.83/365 cos (942.48/365)

    or do I not need to change everything from its previous form?
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