Converting polar and rectangular coordinates

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Discussion Overview

The discussion centers on converting between polar and rectangular coordinates, including specific examples and the conventions used in these coordinate systems. The scope includes mathematical reasoning and conceptual clarification related to coordinate transformations.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant states the relationships between polar and rectangular coordinates, providing the equations for conversion.
  • Another participant suggests substituting specific values into the equations to compute the desired coordinates.
  • A question is raised about the order of the coordinates in polar representation, specifically whether it is (r, theta) or the other way around.
  • A participant clarifies that conventionally, r is the first coordinate in polar coordinates.
  • It is noted that when converting polar coordinates for complex numbers, the x coordinate represents the real part and the y coordinate represents the imaginary part, while maintaining the same conversion principles.

Areas of Agreement / Disagreement

Participants generally agree on the conventions of polar and rectangular coordinates, but there is a question regarding the order of the coordinates that remains unresolved.

Contextual Notes

Some assumptions about the definitions of the coordinates and the context of their application may be missing, which could affect the clarity of the discussion.

Who May Find This Useful

Individuals interested in mathematics, particularly those studying coordinate systems and transformations, may find this discussion beneficial.

Entropee
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So I know x=(r)cos(theta)
and y=(r)sin(theta)

As well as r^2 = x^2 + y^2
And (theta)=tan^-1 y/x or sin^-1 y/r or cos^-1 x/r

If I want to convert the polar coordinates (7.6 , 285(degrees)) to rectangular coordinates, to the nearest hundredth, what would I do?

And also if I were converting the rectangular coordinates (2.4 , 1.8) to polar.


So which variable is which in the coords? so i can plug these in and figure them out...
 
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Put the particular values into their appropriate places in the given equations, and solve for/compute the desired quantities.
 
Is it (r , theta)
or the other way around
 
Conventionally, r is the first coordinate.
 
If you're going from polar to rectangular for complex numbers, the x coordinate usually denotes the real part while the y coordinate denotes the imaginary part. Apart from that it's the same thing.
 
Thanks guys I think i got it :P
This is the best website ever, can't wait to start college next year :P
 

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