Question about cylindrical (ie. 3d polar) coordinate system.

In summary, the equation x^2 + y^2 + z^2 = 4 can be converted to cylindrical coordinates by using the relationship r^2 = x^2 + y^2. However, this does not simplify the equation, and it is not necessary to do so.
  • #1
glog
17
0
Question Details:

Convert the following equation into cylindrical coordinates...
x^2 + y^2 + z^2 = 4

It's obvious that r^2 = x^2+y^2... but that would only simplify the equation to:
r^2 + z^2 = 4 ... is there a better way to do this?
 
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  • #2
That's all you need to do. Your result is in cylindrical coordinates.
 
  • #3
glog said:
Question Details:

Convert the following equation into cylindrical coordinates...
x^2 + y^2 + z^2 = 4

It's obvious that r^2 = x^2+y^2... but that would only simplify the equation to:
r^2 + z^2 = 4 ... is there a better way to do this?

A better way to do what? The problem you stated was "convert the equation to cylindrical coordinates" and you did that. If you are concerned that it in not "simplified" enough, the problem did NOT say "simplify" it!
 

FAQ: Question about cylindrical (ie. 3d polar) coordinate system.

What is a cylindrical coordinate system?

A cylindrical coordinate system is a way of representing points in three-dimensional space using three coordinates: radius, angle, and height. It is often used to describe objects with cylindrical symmetry, such as pipes or columns.

How is the cylindrical coordinate system different from the Cartesian coordinate system?

In the cylindrical coordinate system, the coordinates are represented by radius, angle, and height, whereas in the Cartesian coordinate system, they are represented by x, y, and z coordinates. Additionally, the cylindrical coordinate system uses polar angles and distances, while the Cartesian coordinate system uses Cartesian axes.

What is the relationship between cylindrical and spherical coordinate systems?

Cylindrical and spherical coordinate systems are both ways of representing points in three-dimensional space. In fact, the cylindrical coordinate system is a special case of the spherical coordinate system, where the angle is fixed at 90 degrees.

How do you convert between cylindrical and Cartesian coordinates?

To convert from cylindrical coordinates (r, θ, h) to Cartesian coordinates (x, y, z), you can use the following equations:x = r cos(θ)y = r sin(θ)z = h

What are some real-world applications of the cylindrical coordinate system?

The cylindrical coordinate system is commonly used in engineering and physics to describe objects with cylindrical symmetry, such as pipes, columns, and turbines. It is also used in navigation and astronomy to describe the position of objects in space.

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