Changing rectangular coordinates to polar coordinates ?

[rclakmal]

Homework Statement

Hey i know that we can change it by using
r^2=X^2+y^2
and
tan(theta)=y/x;

but finding some problems in converting the area surrounded by
X=0; Y=0; x+y=1; x+y=2 to polar coordinates .

yr of course you can convert X=0 to theta=pi/2 and Y=0 to theta=0;


But i don't how to convert other 2 boundaries to polar coordinates.Can anyone help me

 

[Cyosis]

Polar coordinates are given by $x=r \cos \theta, y=r \sin \theta, r=x^2+y^2$.

 

[Mark44]

You can convert rectangular coordinates to polar form, and vice versa. Here is a summary of the conversion formulas going both ways.

Convert rectangular to polar

$$r = \pm \sqrt{x^2 + y^2}$$
$$\theta = tan^{-1} (y/x)$$

Convert polar to rectangular
$$x = r cos(\theta)$$
$$y = r sin(\theta)$$

 

[rclakmal]

yr of course i know those two equations !and i have been successful in converting two boundaries of the region .But my problem is how to convert X+Y=1 and X+Y=2 to polar coordinates.
I hope u guys got my question !

 

[Dick]

Then use those equations. Substitute them into x+y=1 and x+y=2 and solve for r to get the upper and lower bounds for the r integration in terms of theta.

 

[rclakmal]

ah ok i got it now thanks !

 

[Mark44]

yr of course i know those two equations

If you look carefully, you'll see that there are four equations.