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Math Help - Extrema polar function

  1. #1
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    Extrema polar function

    I need to find the point on rē = 4cos(2Ɵ) with the highest y-coordinate. I tried this using Lagrange multipliers, but I guess something went wrong during my calculation because when i sketch this polar graph, my point doesn't seem to fit. Can someone please check (and if possible, correct) this? Thanks!
    Attached Thumbnails Attached Thumbnails Extrema polar function-berek1.png   Extrema polar function-berek2.png  
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  2. #2
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    Re: Extrema polar function

    second page ...

    g(r,\theta) = 8\sin^2{\theta} - 4\color{red}\cos(2\theta)

    g(r,\theta) = 8\sin^2{\theta} - 4\color{red}(1 - 2\sin^2{\theta})

    g(r,\theta) = 16\sin^2{\theta} - 4

    g(r,\theta) = 4(4\sin^2{\theta} - 1)
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  3. #3
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    Re: Extrema polar function

    Thank you! Stupid mistake... I found that this point is (sqrt(3/2), 1/sqrt(2)) and (-sqrt(3/2), 1/sqrt(2)) !
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