How to Calculate Maximum Error in Polar Coordinates

[Bryon]

Homework Statement

Rectangular to Polar Coordinates:
I am to find the approximate maximum error in measuring the polar coordinates of the point (7.2, 2.5). There is a possible error of 0.05 in each coordinate.

Homework Equations

dx = deltax
dy = deltay

dz = (partial diff of z with respect to x)dx + (partial diff of z with respect to y)dy

Not sure if I need the following:
x = rcos(theta)
y = rsin(theta)
tan(theta) = y/x

The Attempt at a Solution

I suspect that dx = dy = 0.05

I could set the rectangular coordinates to the polar conversions but I am not sure how that helps:

7.2 = rcos(theta)
2.5 = rsin(theta)

This is where I am held up at and not sure how to go about solving this one.

 

[planck42]

What are dr and $$d\theta$$ in terms of dx and dy?

 

[Bryon]

Would I be differentiating r = y/sin(theta) theta = arcin(y/r) and r = x/cos(theta) theta = arccos(x/r)?

 

[planck42]

Would I be differentiating r = y/sin(theta) theta = arcin(y/r) and r = x/cos(theta) theta = arccos(x/r)?

Close, but get the r's out of your $$\theta$$ formulas and the $$\theta$$'s out of your r formulas.

 

[Bryon]

Ah, all I have to do is substitute r for r = y/sin(theta) in theta = arcsin(y/r) which would be
theta = arcsin(y/ysin(theta)) and so on! Thanks!

 

[planck42]

No, you need the r's and $$\theta$$'s entirely in terms of the original Cartesian coordinates.

 

[Bryon]

I figured it out! Thank you very much!