Spherical Coordinate System

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The spherical coordinate system is very similar to the polar coordinate system used in 2 dimensional graphs, but is instead used in 3 dimensional graphs. Locations within the system are defined using two angles ( and ) and a radius value (). The placement of these angles in relation to the axis can very depending on the field you are working in (see Wikipedia for details), but in math it is defined as the following:

Image Credit: Dmcq, for Wikipedia

- length of the "arm" set by the angles and .

Common shapes:

• Sphere:
• Cylinder:
• Cone:

They spherical coordinates can be helpful when working with triple integrals and solids of a spherical shape.

See Multivariable Calculus Notes - Chapter 15 - Sections 6-8 and trigonometry for more information.