#### Title

#### Description

The spherical coordinates of a point p can be obtained by the following geometric construction. The value of r represents the distance from the point p to the origin (which you can put wherever you like). The value of ✓ is the angle between the positive z-axis and a line l drawn from the origin to p. The value of " is the angle made with the x-axis by the projection of l into the x-y plane (z = 0). Note: for points in the x-y plane, r and " (not ✓) are polar coordinates. The coordinates (r, ✓, ") are called the radius, polar angle, and azimuthal angle of the point p, respectively. It should be clear why these coordinates are called spherical. The points r = a, with a = constant, lie on a sphere of radius a about the origin. Note that the angular coordinates can thus be viewed as coordinates on a sphere. Indeed, they label latitude and longitude.

#### Publication Date

8-2014

#### Keywords

spherical coordinate, transformation, polar change, chapter 13

#### Disciplines

Physical Sciences and Mathematics | Physics

#### Recommended Citation

Torre, Charles G., "13 Spherical Coordinates" (2014). *Foundations of Wave Phenomena*. 10.

http://digitalcommons.usu.edu/foundation_wave/10

## Comments

Version 8.2

Chapter 13