Given rē = 4cos(2Ɵ) , 0<Ɵ<π/4

Calculate the point on this curve with the highest y-coordinate.

How would you calculate this? I do not even know how to start this :(

Thanks already!

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- December 21st 2012, 10:13 AMjones123Extrema polar equation
Given rē = 4cos(2Ɵ) , 0

__<__Ɵ__<__π/4

Calculate the point on this curve with the highest y-coordinate.

How would you calculate this? I do not even know how to start this :(

Thanks already! - December 21st 2012, 06:54 PMchiroRe: Extrema polar equation
Hey jones123.

Hint: How do you represent the (x,y) co-ordinates given the polar representation? - December 21st 2012, 07:02 PMskeeterRe: Extrema polar equation
you're going to have to determine where in the given interval ... this will require doing the grunt work of finding both and .

Derivatives of polar equations are a P-I-T-A. - December 22nd 2012, 05:30 AMjones123Re: Extrema polar equation
- December 22nd 2012, 05:53 AMHallsofIvyRe: Extrema polar equation
Good. Now, differentiate that with respect to x and set y' equal to 0.

Another way to do this, without converting to Cartesian coordinates, is to maximise subject to the constraint , perhaps using Lagrange multipliers. - December 22nd 2012, 08:24 AMskeeterRe: Extrema polar equation

- December 23rd 2012, 06:38 AMjones123Re: Extrema polar equation
- December 23rd 2012, 07:11 AMskeeterRe: Extrema polar equation

Quote:

If rē = 4cos(2Ɵ) than r = sqrt(4cos(2Ɵ)), shouldn't the derivative dr/dƟ be - 8sin(2Ɵ) / 2sqrt(cos(2Ɵ)) ?