How can I convert coordinates from Spherical to Cartesian?

In summary, the conversation discusses the spherical coordinate system and the differences between it and the Cartesian coordinate system. The main concept in the spherical coordinate system is the use of magnitude and angle to describe a point, compared to the x and y coordinates in Cartesian. The conversation also mentions using Wikipedia and other resources for further understanding. Finally, the conversation touches on converting between spherical and Cartesian coordinates using the formula φ = arctan (y/x) and provides an example of how to do so.
  • #1
Mathysics
37
0
I do not understand Spherical coordinate system.

I'm asked to compare the differences with Cartesian coordinate but I have no idea how to start.

So I would like some help that will at least give me a understanding of the spherical coordinate system, thx
 
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  • #2
Let's stick to the 2-d case first. That means we compare Cartesian coordinates with polar coordinates. In Cartesian you need an x coordinate and a y coordinate to describe a fixed point on the grid. How do you describe such a point in polar coordinates?
 
  • #3
Cyosis said:
Let's stick to the 2-d case first. That means we compare Cartesian coordinates with polar coordinates. In Cartesian you need an x coordinate and a y coordinate to describe a fixed point on the grid. How do you describe such a point in polar coordinates?
(magnitude,angle)

The task is to investigate the spherical coordinate system, which I haven't learn but I have no idea what to do
 
  • #4
Yes it's the distance to that point and an angle. Keeping the distance to a point constant while rotating the angle 2pi rad you will get a circle. How can you extend this system so that instead of a circle you get a sphere?
 
  • #5
Wikipedia and Wolfram's Mathworld have pretty good pages on spherical coordinates, I would suggest that you try having a look there.
 
  • #6
Mathysics said:
I'm now starting to understand more about spherical coordinate system. I had been researching information about spherical coordinate system but now I am stuck again :)

To convert φ from Spherical to Cartesian we can use φ = arctan (y/x)

The problem is... I don't know how to do arctan so I like some help again.

If my points are (3,4,5) how can i convert that into φ using the formula above?
You put those numbers into the formula and do exactly what the formula says! y= 4 and x= 3 so y/x= 4/3. What is arctan(4/3)?
 

1. What is a spherical coordinate system?

A spherical coordinate system is a three-dimensional coordinate system used to locate points on the surface of a sphere. It uses two angles, typically denoted as θ (theta) and φ (phi), and a distance or radius, denoted as r, to define the position of a point.

2. How is a spherical coordinate system different from a Cartesian coordinate system?

In a Cartesian coordinate system, points are located using three perpendicular axes (x,y,z) and distances along those axes. In a spherical coordinate system, points are located using two angles and a radius, making it better suited for describing spherical objects.

3. What are the ranges of the angles and radius in a spherical coordinate system?

The angle θ ranges from 0 to 180 degrees, while the angle φ ranges from 0 to 360 degrees. The radius can range from 0 to infinity.

4. How is a point converted from Cartesian coordinates to spherical coordinates?

To convert a point from Cartesian coordinates (x,y,z) to spherical coordinates (r,θ,φ), the following equations can be used:
r = √(x² + y² + z²)
θ = arccos(z/r)
φ = arctan(y/x)

5. What are some applications of spherical coordinate systems?

Spherical coordinate systems are commonly used in fields such as astronomy, physics, and engineering to describe the position and motion of objects on a curved surface. They are also used in navigation and mapping, as well as in computer graphics for creating 3D models of spherical objects.

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