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Can you use cylindrical coordinates for a sphere?

Can you use cylindrical coordinates for a sphere?

To convert a point from cylindrical coordinates to spherical coordinates, use equations ρ=√r2+z2,θ=θ, and φ=arccos(z√r2+z2).

How do you convert spherical coordinates to cylindrical coordinates?

To convert a point from spherical coordinates to cylindrical coordinates, use equations r=ρsinφ,θ=θ, and z=ρcosφ.

How do you find the coordinates of a sphere?

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

Are polar coordinates the same as cylindrical?

Cylindrical coordinates are a simple extension of the two-dimensional polar coordinates to three dimensions. The polar coordinate r is the distance of the point from the origin. The polar coordinate θ is the angle between the x-axis and the line segment from the origin to the point.

How do you find cylindrical coordinates?

To form the cylindrical coordinates of a point P, simply project it down to a point Q in the xy-plane (see the below figure). Then, take the polar coordinates (r,θ) of the point Q, i.e., r is the distance from the origin to Q and θ is the angle between the positive x-axis and the line segment from the origin to Q.

What is Rho in spherical coordinates?

The coordinates used in spherical coordinates are rho, theta, and phi. Rho is the distance from the origin to the point. Theta is the same as the angle used in polar coordinates. Phi is the angle between the z-axis and the line connecting the origin and the point.

What is a sphere in spherical coordinates?

A sphere that has the Cartesian equation x2 + y2 + z2 = c2 has the simple equation r = c in spherical coordinates. Two important partial differential equations that arise in many physical problems, Laplace’s equation and the Helmholtz equation, allow a separation of variables in spherical coordinates.

How do you find the cylindrical coordinate system?