Changing rectangular coordinates to polar coordinates ?

In summary, polar coordinates can be converted to rectangular coordinates and vice versa using specific formulas. To convert rectangular coordinates to polar coordinates, use the formula r = \pm \sqrt{x^2 + y^2} and \theta = tan^{-1} (y/x). To convert polar coordinates to rectangular coordinates, use the formulas x = r cos(\theta) and y = r sin(\theta). These formulas can be used to convert the area surrounded by X=0; Y=0; x+y=1; x+y=2 to polar coordinates. The upper and lower bounds for the r integration can be determined by substituting the equations into x+y=1 and x+y=2 and solving for r in terms of theta.
  • #1
rclakmal
76
0

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
 
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  • #2
Polar coordinates are given by [itex]x=r \cos \theta, y=r \sin \theta, r=x^2+y^2[/itex].
 
  • #3
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

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

Convert polar to rectangular
[tex]x = r cos(\theta)[/tex]
[tex]y = r sin(\theta)[/tex]
 
  • #4
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 !
 
  • #5
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.
 
  • #6
ah ok i got it now thanks !
 
  • #7
rclakmal said:
yr of course i know those two equations
If you look carefully, you'll see that there are four equations.
 

1. How do I convert rectangular coordinates to polar coordinates?

To convert from rectangular coordinates (x, y) to polar coordinates (r, θ), use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)

2. What is the purpose of changing from rectangular to polar coordinates?

The purpose of converting from rectangular to polar coordinates is to represent points in a two-dimensional space in a different coordinate system. This can be helpful in certain calculations or when graphing certain equations.

3. Can negative values be used in polar coordinates?

Yes, negative values can be used in polar coordinates. The radius (r) can be negative, indicating a point on the opposite side of the pole (center). The angle (θ) can also be negative, indicating a point in the opposite direction from the reference angle.

4. How do I convert polar coordinates to rectangular coordinates?

To convert from polar coordinates (r, θ) to rectangular coordinates (x, y), use the following formulas:
x = r cos(θ)
y = r sin(θ)

5. What is the difference between polar and rectangular coordinates?

Polar coordinates use a distance (radius) and angle from a reference point (pole) to represent a point in a two-dimensional space. Rectangular coordinates use two perpendicular distances (x and y) from a reference point (origin) to represent a point in a two-dimensional space.

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