## anonymous one year ago c

1. anonymous

sorry, r = 2cos(phi) is an equation in spherical coordinates where phi is the polar angle, 0 <phi <pi

2. anonymous

it is an equation of a sphere in spherical coordinates, need it in rectangular coordinates

3. phi

usually people use rho rather than "r" (and use r for cylindrical coords)

4. ganeshie8

$$\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z$$ Next replace $$\rho^2$$ by $$x^2+y^2+z^2$$ and you're done!

5. anonymous

My apologies, I am still learning the coordinate systems and standard notation. phi is the polar angle in spherical coordinates which is between zero and pi

6. ganeshie8

|dw:1439995254724:dw|

7. ganeshie8

Notice that in below triangle, we have $$z = \rho\cos\phi$$ |dw:1439995296915:dw|

8. anonymous

ganeshie8 thank you for your help. I see now that I can complete the square on z^2 - 2z to get a nice cartesian equation

9. ganeshie8

$$\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z$$ replacing $$\rho^2$$ by $$x^2+y^2+z^2$$ gives $x^2+y^2+z^2=2z$ that is the cartesian form...

10. ganeshie8

and yeah you may complete the square for $$z^2-2z$$ to get a nicer one :)