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Math Help - Trigonometry and derivative

  1. #1
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    Trigonometry and derivative

    The rule says that if the first derivative(x) > 0 then it is increasing at that point and if the first derivative(x) < 0 then it is decreasing at that point.
    I analyzed function f(x)=4*(sin(x))^2
    f'=8*sin(x)*cos(x)
    The function f(x) should increase at 150 degrees but the first derivative at 150 is < 0. Graph shows that this function increases at 150 degrees.
    Why does not the first derivative show it ?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by totalnewbie
    The rule says that if the first derivative(x) > 0 then it is increasing at that point and if the first derivative(x) < 0 then it is decreasing at that point.
    I analyzed function f(x)=4*(sin(x))^2
    f'=8*sin(x)*cos(x)
    The function f(x) should increase at 150 degrees but the first derivative at 150 is < 0. Graph shows that this function increases at 150 degrees.
    Why does not the first derivative show it ?
    Examine f(x) again - it is decreasing at x=150 degrees.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by totalnewbie
    The rule says that if the first derivative(x) > 0 then it is increasing at that point and if the first derivative(x) < 0 then it is decreasing at that point.
    I analyzed function f(x)=4*(sin(x))^2
    f'=8*sin(x)*cos(x)
    The function f(x) should increase at 150 degrees but the first derivative at 150 is < 0. Graph shows that this function increases at 150 degrees.
    Why does not the first derivative show it ?
    Also, avoid using degrees in this sort of problem, the derivatives of the trig
    functions you are familiar with are for the functions with the argument in
    radians.

    RonL
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  4. #4
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    Quote Originally Posted by CaptainBlack
    Also, avoid using degrees in this sort of problem, the derivatives of the trig
    functions you are familiar with are for the functions with the argument in
    radians.

    RonL
    It depends on DRG. I use DEG mode. If I used RAD mode, I would have to use radians.
    Anyway the problem is solved.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by totalnewbie
    It depends on DRG. I use DEG mode. If I used RAD mode, I would have to use radians.
    Anyway the problem is solved.
    The "units" of f' are they "per radian" or "per degree"?

    You are setting yourself up to make mistakes is you mix up how
    you are measuring angles.

    In your equation "f(x)=4*(sin(x))^2" the x is almost always in
    radians.

    RonL
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  6. #6
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    I'm going to poke my nose in and say in another way what CaptainBlack is trying to say:
    You can certainly do your trig functions in DEGREE mode, but the Calculus formulas for the derivatives are done in RADIANS. So if you are using degrees to calculate your angles you have to introduce extra factors in the Calculus formulas to get the correct answers.

    It is MUCH safer to use radians when doing Calculus.

    -Dan
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