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Math Help - differentiation in trigonomerty help???

  1. #1
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    differentiation in trigonomerty help???

    T = 10Sin ( (2Pi/365)*X ) + 25 , is the daily average temperature in a village where X is the day of the year.

    I have constructed a table of values for 0 < X < 365 and created a graph, however when it comes to differentiating the following I am a bit lost. If someone could talk me through it that would be great:


    i) The rate of change of the temperature is given by dT/dX . Find dT/dX and the rate of change of the temperature when X = 150 .
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by bobbymellor View Post
    T = 10Sin ( (2Pi/365)*X ) + 25 , is the daily average temperature in a village where X is the day of the year.

    I have constructed a table of values for 0 < X < 365 and created a graph, however when it comes to differentiating the following I am a bit lost. If someone could talk me through it that would be great:


    i) The rate of change of the temperature is given by dT/dX . Find dT/dX and the rate of change of the temperature when X = 150 .
    By chain rule, T=10\sin\left(\frac{2\pi}{365}X\right)+25\implies \frac{\,dT}{\,dX}=10\cos\left(\frac{2\pi}{365}X\ri  ght)\cdot\frac{\,d}{\,dX}\left[\frac{2\pi}{365}X\right]

    Can you continue and find T^{\prime}\!\left(150\right)??
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  3. #3
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    Hi again, coming back to this problem, honestly I'm still a bit lost when it comes to differentiating anything but the very basic examples, Im very comfortable with anything trig' based but still having problems with differentiation.
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