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Math Help - Trig Derivative Q

  1. #1
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    Trig Derivative Q

    Find points on the function f(x) = 2sinx + sin²x for when the tangent line is horizontal.

    ---------

    so i found the derivative of that function, which is
    f'(x) = 2cosx + 2sinxcosx

    what do i do now? set f'(x) to 0? i tried that, but the answer key says that the answer is

    (π/2 + 2nπ, 3), (3π/2 + 2nπ, -1)

    what does that notation mean? i am confused.. thx
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  2. #2
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    Quote Originally Posted by mneox View Post
    Find points on the function f(x) = 2sinx + sin²x for when the tangent line is horizontal.

    ---------

    so i found the derivative of that function, which is
    f'(x) = 2cosx + 2sinxcosx

    what do i do now? set f'(x) to 0? i tried that, but the answer key says that the answer is

    (π/2 + 2nπ, 3), (3π/2 + 2nπ, -1)

    what does that notation mean? i am confused.. thx
    f'(x) = 2\cos{x}(1 + \sin{x})

    the base solutions in the interval [0, 2\pi] are ...

    \cos{x} = 0 ... x = \frac{\pi}{2} \, , \, \frac{3\pi}{2}

    \sin{x} = -1 ... x = \frac{3\pi}{2}

    the + 2n\pi includes all the other solutions that are coterminal with the base solutions.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    f'(x) = 2\cos{x}(1 + \sin{x})

    the base solutions in the interval [0, 2\pi] are ...

    \cos{x} = 0 ... x = \frac{\pi}{2} \, , \, \frac{3\pi}{2}

    \sin{x} = -1 ... x = \frac{3\pi}{2}

    the + 2n\pi includes all the other solutions that are coterminal with the base solutions.
    thanks, i get that part now, but do you know what the 3 and -1 mean? How did those y-values come about?
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  4. #4
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    Quote Originally Posted by mneox View Post
    thanks, i get that part now, but do you know what the 3 and -1 mean? How did those y-values come about?
    plug the x-value solutions into the original function.
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