## What is the relation between spherical and Cartesian coordinates?

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In summary, the formulas for Cartesian coordinates in terms of spherical coordinates are x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ.

**What is Cartesian form of spherical form?**

A sphere that has Cartesian equation x 2 + y 2 + z 2 = c 2 x 2 + y 2 + z 2 = c 2 has the simple equation ρ = c in spherical coordinates.

**How do you plot spherical coordinates?**

Count 4 units outward in the positive direction from the origin on the horizontal axis. from the horizontal axis (again, as with polar coordinates). Imagine a single longitude line arcing from the north pole of a sphere through the point on the equator where you are right now and onward to the south pole.

### How do you describe a sphere in spherical coordinates?

In the spherical coordinate system, a point P in space is represented by the ordered triple (ρ,θ,φ), where ρ is the distance between P and the origin (ρ≠0),θ is the same angle used to describe the location in cylindrical coordinates, and φ is the angle formed by the positive z-axis and line segment ¯OP, where O is the …

**What is theta in Cartesian coordinates?**

The Greek letter θ (theta) is often used to denote an angle, and a polar coordinate is conventionally referred to as (r, θ) instead of (x, y). Thus, when dealing with polar coordinates, we’ll now use “theta” as the preferred variable name for the angle.

**Where is spherical coordinate system used?**

Spherical coordinates of the system denoted as (r, θ, Φ) is the coordinate system mainly used in three dimensional systems. In three dimensional space, the spherical coordinate system is used for finding the surface area. These coordinates specify three numbers: radial distance, polar angles and azimuthal angle.

## How do you convert spherical coordinates to Cartesian coordinates?

Conversely spherical coordinates may be converted to Cartesian coordinates using the following formulas: x = r sin ( φ) cos ( θ) y = r sin ( φ) sin ( θ) z = r cos ( φ) \\displaystyle \\begin {aligned} x &= r\\sin\\left (\\varphi\\right) \\cos\\left (\heta\\right) \\\\ \\\\ y &= r\\sin\\left (\\varphi\\right) \\sin\\left (\heta\\right)

**What is the right-handed basis of the spherical coordinate system?**

We can either work with this as a left-handed basis, or re-order the coordinates to give the right-handed basis ( ^ e r, ^ e ϕ, ^ e θ) ( e ^ r, e ^ ϕ, e ^ θ) . If the spherical coordinates change with time then this causes the spherical basis vectors to rotate with the following angular velocity.

**How do spherical coordinates affect the rotation of the basis vectors?**

If the spherical coordinates change with time then this causes the spherical basis vectors to rotate with the following angular velocity. Changing r r does not cause a rotation of the basis, while changing θ θ rotates about the vertical axis ^ k k ^ and changing ϕ ϕ rotates about ^ e θ e ^ θ.

### What is the correct order of spherical coordinates?

Although it is common to write the spherical coordinates in the order ( r, θ, ϕ) ( r, θ, ϕ), this order gives a left-handed basis ( ^ e r, ^ e θ, ^ e ϕ) ( e ^ r, e ^ θ, e ^ ϕ), which we can see graphically from the fact that ^ e r × ^ e θ = − ^ e ϕ e ^ r × e ^ θ = − e ^ ϕ.