- #1
robertjford80
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Homework Statement
Do you see how y gets converted to csc? I don't get that. I would y would be converted to sin in polar coordinates.
Converting cartesian to polar coordinates in multiple integrals
- Thread starter robertjford80
- Start date
In summary, the conversation was about understanding the conversion of y to csc in polar coordinates and clarifying the integration of x in the yellow region. The picture provided was helpful in understanding the concept and the conversation ended with the person expressing their appreciation for the explanation.
Do you see how y gets converted to csc? I don't get that. I would y would be converted to sin in polar coordinates.
- #2
Karamata
- 60
- 0
<deleted>
- #3
robertjford80
- 388
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thanks, I got it.
- #4
robertjford80
- 388
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I need to see what Karmata wrote again, if anyone knows I would appreciate it.
- #5
robertjford80
- 388
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still needing
- #6
Karamata
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Hi robertjford80!
I deleted my post because there was error in him (oh, bad English)
But, look at picture.
They said [itex]\int_0^6 \int_0^y x \mbox{d}x\mbox{d}y[/itex], that is yellow region (x from 0 (parallel y-axes) to x=y, y from 0 to 6). [itex]r[/itex] is moving from [itex]r=0[/itex] to y=6, so, [itex] y= 6= r \sin \theta \Rightarrow r = \dfrac{6}{\sin \theta} = 6 \csc \theta[/itex]
I deleted my post because there was error in him (oh, bad English)
But, look at picture.
They said [itex]\int_0^6 \int_0^y x \mbox{d}x\mbox{d}y[/itex], that is yellow region (x from 0 (parallel y-axes) to x=y, y from 0 to 6). [itex]r[/itex] is moving from [itex]r=0[/itex] to y=6, so, [itex] y= 6= r \sin \theta \Rightarrow r = \dfrac{6}{\sin \theta} = 6 \csc \theta[/itex]
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- #7
robertjford80
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ok, thanks, I got it. this so far has been one of the most difficult concepts in calculus to understand but I'm slowly getting it.
Related to Converting cartesian to polar coordinates in multiple integrals
What are cartesian and polar coordinates?
Cartesian coordinates, also known as rectangular coordinates, are a system for representing points in a plane using two perpendicular axes. Polar coordinates, on the other hand, use a radius and angle to locate a point on a plane. They are both commonly used in mathematics and physics.
Why would I need to convert from cartesian to polar coordinates in multiple integrals?
In many cases, it is easier to solve problems using polar coordinates, especially when dealing with circular or symmetric shapes. Converting to polar coordinates can simplify the integration process and make it easier to find the solution.
How do I convert from cartesian to polar coordinates?
To convert from cartesian to polar coordinates, you can use the following formulas:
x = rcosθ
y = rsinθ
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.
Can I convert from polar to cartesian coordinates in multiple integrals?
Yes, it is possible to convert from polar to cartesian coordinates in multiple integrals by using the inverse of the formulas mentioned above. The conversion process may vary depending on the specific problem, so it is important to understand the underlying principles and have a good grasp of both coordinate systems.
Are there any tips for converting from cartesian to polar coordinates in multiple integrals?
One tip for converting from cartesian to polar coordinates in multiple integrals is to first sketch the region of integration and identify any symmetries that can simplify the conversion process. It is also helpful to practice and familiarize yourself with the conversion formulas and their applications in different types of problems.
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