MHB How to Convert Polar to Rectangular Coordinates in Calculus?

  • Thread starter Thread starter karush
  • Start date Start date
  • Tags Tags
    Polar Rectangular
AI Thread Summary
To convert polar coordinates to rectangular coordinates for the equation r = 3 - cos(θ), the relationship r² = x² + y² is essential. The equation can be manipulated to x² + y² = 3r - x, leading to x² + y² = 3√(x² + y²) - x. This results in the equation (x² + x + y²)² = 9(x² + y²), which can be complex to simplify. The discussion highlights the challenges in handling the conversion, emphasizing that intuition can sometimes guide correct answers. Overall, the conversion process can be intricate and requires careful algebraic manipulation.
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
$r=3-\cos\left({\theta}\right)$
${r}^{2}=3r-r\cos\left({\theta}\right)$
${x}^{2}+{y}^{2}=3r+x$
How you deal with 3r ?
 
Mathematics news on Phys.org
karush said:
$r=3-\cos\left({\theta}\right)$
${r}^{2}=3r-r\cos\left({\theta}\right)$
${x}^{2}+{y}^{2}=3r+x$
How you deal with 3r ?
You have a slight mistake: [math]x^2 + y^2 = 3r - x[/math]

As always [math]r = \sqrt{x^2 + y^2}[/math].

Continuing:
[math]x^2 + y^2 = 3 \sqrt{x^2 + y^2} - x[/math]

[math]x^2 + x + y^2 = 3 \sqrt{x^2 + y^2}[/math]

[math]\left ( x^2 + x + y^2 \right ) ^2 = 9(x^2 + y^2)[/math]

etc.

Yes, it's ugly.

-Dan
 
Last edited by a moderator:
Funny I had that answer and thot it was wrong, quess intuition is always right?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top