# Identifying and graphing a surface in spherical coordinates

• Oct 7th 2007, 03:32 PM
Undefdisfigure
Identifying and graphing a surface in spherical coordinates
I have a variable equivalent to z in sphereical coordinates which is a circle with a line down the middle (I think its called gamma but I could be wrong, too lazy to look it up right now). Gamma equals Pi/3. Gamma is also an angle between 0x and the z-axis. How do I graph the surface represented by this spherical equation?
• Oct 7th 2007, 03:43 PM
Jhevon
Quote:

Originally Posted by Undefdisfigure
I have a variable equivalent to z in sphereical coordinates which is a circle with a line down the middle (I think its called gamma but I could be wrong, too lazy to look it up right now). Gamma equals Pi/3. Gamma is also an angle between 0x and the z-axis. How do I graph the surface represented by this spherical equation?

in spherical coordinates we use the variables:

$\displaystyle \rho$: rho
$\displaystyle \theta$: theta, and
$\displaystyle \phi$: phi

now restate your question with the proper variable names so we know what you are talking about
• Oct 7th 2007, 05:56 PM
Undefdisfigure
The variable equivalent to z from what I see in your reply is phi. The answer given by the book "Multivariable Calculus 6th Edition" by James Stewart is a half cone. When I tried to make the graph myself it appeared to me to be a half plane because of the angle it formed with the z-axis. Obviously I was wrong. Do I have to do some spherical to Cartesian or vice versa transformations before I have the information necessary to draw the surface?
• Oct 7th 2007, 06:11 PM
Jhevon
Quote:

Originally Posted by Undefdisfigure
The variable equivalent to z from what I see in your reply is phi. The answer given by the book "Multivariable Calculus 6th Edition" by James Stewart is a half cone. When I tried to make the graph myself it appeared to me to be a half plane because of the angle it formed with the z-axis. Obviously I was wrong. Do I have to do some spherical to Cartesian or vice versa transformations before I have the information necessary to draw the surface?

they have a 6th edition now?! i have the 5th edition of that text, maybe the problem is the same. what chapter and problem are you doing?
• Oct 7th 2007, 06:51 PM
Undefdisfigure
I'm doing section 16.8 #5. When I said pi/3, I meant pi (or pie if that's the way you spell it) as in 3.14. Take note that this is multrivariable, so it is an extension of the single variable book. I'm sure you must have both though Jhevon.
• Oct 7th 2007, 07:10 PM
Jhevon
Quote:

Originally Posted by Undefdisfigure
I'm doing section 16.8 #5. When I said pi/3, I meant pi (or pie if that's the way you spell it) as in 3.14.

it's spelt pi. that is not the same question in my book, i guess the difference in editions account for that. in my book, 16.8 #5 asks you to set up a triple integral over the solid shown, and the solid for #5 looks like a thick pizza slice bounded in the first quad. anyway, you seem to be asking me how to graph $\displaystyle \phi = \pi$ (by the way $\displaystyle \phi$ is not equivalent to $\displaystyle z$)

but anyway, i need to know what $\displaystyle \rho$ and $\displaystyle \theta$ are, was the question accompanied by a figure?

if $\displaystyle \theta = 2 \pi$ and $\displaystyle \rho = c$, for c a constant

then $\displaystyle \phi = \pi$ is a sphere with center the origin and radius
$\displaystyle c$.

Quote:

Take note that this is multrivariable, so it is an extension of the single variable book. I'm sure you must have both though Jhevon.
i have the combined book, single and multivariable in one! (Cool)