How do you change (0,3,-3) from rectangular to spherical coordinates?

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Answer 1 · 2015-02-03T19:08:50

The answer is: $(3sqrt2,pi/2,3/4pi)$ .

To change the coordinates from rectangular to spherical we have to use these formulae:

$rho=sqrt(x^2+y^2+z^2)$ ;
$phi=arctan(y/x)$ ;
$theta=arccos(z/sqrt(x^2+y^2+z^2))$ .

So:

$rho=sqrt(0^2+3^2+3^2)=sqrt18=3sqrt2$ ;

$phi=arctan(3/0)=arctan(oo)=pi/2$ ;

$theta=arccos((-3)/sqrt(0^2+3^2+3^2))=arccos(-3/(3sqrt2))=arccos(-1/sqrt2*sqrt2/sqrt2)=arccos(-sqrt2/2)=3/4pi$ .

So the point becomes: $(3sqrt2,pi/2,3/4pi)$ .