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Math Help - finding min and max coordinates within interval

  1. #1
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    finding min and max coordinates within interval

    Hello, my function is x-2cos(x), derived to 1+2sin(x).
    I need to find the local max and min points on the interval [0,2pi]
    Solving for x (sinx=-0.5) I get -pi/6 which is outside of my interval. I therefore ignore that value. My textbook says the two values I need are 7pi/6 an 11pi/6.
    My problem is I cant see how they calculated those two values.
    Can someone please enlighten me !

    Thanks kindly
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  2. #2
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    Crna Gora
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    Re: finding min and max coordinates within interval

    Quote Originally Posted by fran1942 View Post
    Hello, my function is x-2cos(x), derived to 1+2sin(x).
    I need to find the local max and min points on the interval [0,2pi]
    Solving for x (sinx=-0.5) I get -pi/6 which is outside of my interval. I therefore ignore that value. My textbook says the two values I need are 7pi/6 an 11pi/6.
    My problem is I cant see how they calculated those two values.
    Can someone please enlighten me !

    Thanks kindly
    Hint :

    \sin \frac{\pi}{6}=\frac{1}{2} ~\text{and}~ \sin \frac{5 \pi}{6}=\frac{1}{2}

    \sin(\pi + \alpha)=-\sin \alpha
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  3. #3
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    Re: finding min and max coordinates within interval

    Sketch a graph of y=sinx and draw in the line y=-1/2. Since arc sin1/2=pi/6 you will see that the solutions in your range are pi+pi/6 and 2pi-pi/6
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