cylindrical coordinates to 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 + 

Thus, we readily have the conversion formula: x = r cosθ y = r sinθ z = z The reserve formula from Cartesian coordinates to cylindrical coordinates follows from the conversion formula from 2D Cartesian to 2D polar coordi- nates: r2 = x2 + y2 θ = arctan y x or arctan y x + π

Cylindrical coordinates are related to rectangular coordinates as follows r = √ x2 + y2 + z2 The spherical coordinate vectors are defined as er := 1 ∇r ∇r

In the cylindrical coordinate system, a point P in space is represented by the ordered triple (r, θ, z), where r and θ are polar coordinates of the projection of P onto 

The Cylindrical coordinate system is built on the polar coordinate system with the addition of a Spherical coordinates are defined by three parameters: 1)  

Cylindrical and Spherical Coordinates “Non-Rectangular Coordinate Systems in 3-space” In Calculus II, we considered the polar coordinate system to help inte 

Examples of orthogonal coordinate systems include the Cartesian (or rectangular ), the cir- cular cylindrical, the spherical, the elliptic cylindrical, the parabolic 

The Cartesian coordinate system (x, y, z) is the system that we are used to The other two systems, cylindrical coordinates (r, θ, z) and spherical coor- dinates (r 

What is dV in Cylindrical Coordinates? Recall that when integrating in polar coordinates, we set dA = r dr dθ When viewing a small piece of volume, ∆V