Extrema polar function

**jones123** · January 7th 2013, 10:24 AM

I need to find the point on r² = 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!

**skeeter** · January 7th 2013, 02:20 PM

second page ...

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

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

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

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

**jones123** · January 7th 2013, 05:00 PM

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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