My Math Forum Spherical Coordinate Problem

 Calculus Calculus Math Forum

 March 15th, 2009, 04:28 PM #1 Member   Joined: Mar 2009 From: San Bernardino, California Posts: 50 Thanks: 0 Spherical Coordinate Problem I have been studying for a midterm coming up this Thursday in my Calculus class but I'm not particularly good with spherical coordinates. On the study guide he gives this problem: $4z^2=x^2+y^2$----> Convert to spherical coordinates and sketch. Given that: $x=\rho cos \theta sin \phi$ $y=\rho sin \theta sin \phi$ $z=\rho cos \phi$ in a spherical system, I plugged the spherical equivalents and came up with: $tan^2 \phi=4$ $\phi=\pm tan^{-1}(2)$ So from this I thought it must be a right circular cone making an angle of declination of $tan^{-1}(2)$ between the positive z-axis and the xy-plane but in my book, a similar problem, $3z^2=x^2+y^2$ says its a double cone (eg the type conic sections are derived from). Could anyone explain to me why this?
 March 15th, 2009, 05:46 PM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Spherical Coordinate Problem Because phi is plus or minus?
 March 15th, 2009, 05:51 PM #3 Member   Joined: Mar 2009 From: San Bernardino, California Posts: 50 Thanks: 0 Re: Spherical Coordinate Problem Oh wow just duh. I don't know why I had it in my head that $\phi=-tan^{-1}(2)$ was between the positive z-axis and the negative portion of the xy-plane. I'm still getting used to 3D. Thanks.

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