# Extrema polar function

• January 7th 2013, 10:24 AM
jones123
Extrema polar function
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!
• January 7th 2013, 02:20 PM
skeeter
Re: Extrema polar function
second page ...

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

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

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

$g(r,\theta) = 4(4\sin^2{\theta} - 1)$
• January 7th 2013, 05:00 PM
jones123
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)) !