Solve Polar to Cartesian Equation & Identify Graph

  • Thread starter Thread starter RESmonkey
  • Start date Start date
  • Tags Tags
    Cartesian Polar
RESmonkey
Messages
25
Reaction score
0

Homework Statement



Replace the polar equation by an equivalent Cartesian (rectangular) equation. Then identify or describe the graph.

****Let's just make x = theta because I can't find a theta symbol*****

r = 2cos(x) + 2sin(x)


Homework Equations



none?

The Attempt at a Solution



x = rcos(x) = (2cos(x) + 2sin(x)) * cos(x)
y = rsin(x) = (2cos(x) + 2sin(x)) *sin(x)

No idea what do to from here.


Thanks in advance
 
Physics news on Phys.org
Try multiplying r = 2\cos\theta + 2\sin\theta through by r.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top