Converting from Polar to Rectangular

  • Thread starter Thread starter tachu101
  • Start date Start date
  • Tags Tags
    Polar Rectangular
AI Thread Summary
The discussion focuses on converting the polar equation r=3/(4cosθ-sinθ) into rectangular form. The key equations used include r=√(x²+y²), x=rcosθ, and y=rsinθ. The solution process involves eliminating the denominator, leading to the equation 4x-y=3. Participants confirm that this transformation is correct. The conversion successfully translates the polar coordinates into rectangular coordinates.
tachu101
Messages
74
Reaction score
0

Homework Statement



Convert r=3/(4cos\theta-sin\theta) to rectangular form

Homework Equations



r=\sqrt{}x^2+y^2

The Attempt at a Solution



4x-y=3 ?
 
Last edited:
Physics news on Phys.org
Relevant equations: x=rcos0, y=rsin0

All you need to do is get rid of the denominator and you're home free.
 
tachu101 said:

Homework Statement



Convert r=3/(4cos\theta-sin\theta) to rectangular form

Homework Equations



r=\sqrt{}x^2+y^2

The Attempt at a Solution



4x-y=3 ?
Yes, that's correct.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
Back
Top