(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the derivative of the transformation x=rcos(theta), y=rsin(theta).

Then estimate the cartesian coordinates for r=2.2 and theta=pi(1/6-1/60)

3. The attempt at a solution

I found the partials with respect to r and theta for both x and y.

I also wrote down the differentials (i think):

[itex]dx=cos\theta dr-rsin\theta d\theta[/itex]

[itex]dy=sin\theta dr+rcos\theta d\theta[/itex]

So I calculated x(r,theta) at (2,pi/6) then added the value of dx (r,theta,dr,dtheta) at (2,pi/6,.2,-pi/60) and got approx 1.95762. I calculated the x=2.2cos(pi(1/6-1/60)) and got a value very close to that, so I'm assuming I did that part right.

Where I am getting stuck is for the y coordinate.

I used the same exact procedure, but when I add dy to y(2,pi/6) the value increases to 1.00931, instead of decreasing to approx .99878.

My gut tells me I made a sign error somewhere or something, but I can't seem to find it. What am I doing wrong?

Thanks.

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# Homework Help: Estimate using the derivative: Am I making a sign error somewhere?

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