What does X equal in spherical coordinates?

Since r=ρsinϕ, these components can be rewritten as x=ρsinϕcosθ and y=ρsinϕsinθ. In summary, the formulas for Cartesian coordinates in terms of spherical coordinates are x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ.

What is X in Cartesian coordinates?

Plotting Points on a Cartesian Plane A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical.

How do you convert spherical to Cartesian?

To convert a point from spherical coordinates to Cartesian coordinates, use equations x=ρsinφcosθ,y=ρsinφsinθ, and z=ρcosφ. To convert a point from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2).

How do you convert equations from spherical to rectangular coordinates?

x = ρ sin φ cos θ These equations are used to convert from y = ρ sin φ sin θ spherical coordinates to rectangular z = ρ cos φ coordinates.

How are spherical polar coordinates related?

The distance between any arbitrary point and the planes are the coordinates of that point. A coordinate system with a fixed origin and a zenith direction is a spherical coordinate system. The polar angle is the angle from the zenith direction and the line which connects the point with the origin.

Which is the Cartesian equation for spherical coordinates?

Cartesian Cylindrical Spherical Cylindrical Coordinates x = r cosθ r = √x2 + y2 y = r sinθ tan θ = y/x z = z z = z Spherical Coordinates x = ρsinφcosθ ρ = √x2 + y2 + z2 y = ρsinφsinθ tan θ = y/x z = ρcosφ cosφ = √x2 + y2 + z2 z

What do you need to know about spherical coordinates?

Spherical coordinates can take a little getting used to. It’s probably easiest to start things off with a sketch. Spherical coordinates consist of the following three quantities. First there is ρ ρ . This is the distance from the origin to the point and we will require ρ ≥ 0 ρ ≥ 0. Next there is θ θ .

How to convert from Cartesian to cylindrical coordinate system?

Cartesian to Cylindrical First, we have to remember that the z stays the same, so we only have to focus on the xy-plane. r is just the radius of the circle, and $x^2 + y^2 = r^2$, so r = $sqrt(x^2 + y^2)$.

How to find the radius of a sphere?

The first thing we can do find ρ ρ. That’s the radius of the sphere, and it equals x 2 + y 2 + z 2 x 2 + y 2 + z 2.