# Category:Definitions/Spherical Coordinates

This category contains definitions related to Spherical Coordinates.

Related results can be found in **Category:Spherical Coordinates**.

A **spherical coordinate system** is a polar coordinate system in $3$ dimensions.

A distinct point $O$ is identified, and referred to as the origin.

### Polar Axis

The **polar axis** of a **spherical coordinate system** is the vertical straight line which passes through the **origin** $O$.

### Horizontal Axis

Having identified the **polar axis** of a **spherical coordinate system**, one then selects a distinct horizontal straight line, also passing through the origin $O$, perpendicular to the **polar axis**

This horizontal straight line is referred to as the **horizontal axis**.

### Initial Meridian Plane

The **initial meridian plane** of a **spherical coordinate system** is the vertical plane in which the **polar axis** and **horizontal axis** both lie.

Hence, let $P$ be an arbitrary point $P$ in space.

Let $\mathbf r$ be the **radius vector** of $P$ with respect to $O$.

The position of $P$ is specified in **spherical coordinates** by:

- $(1): \quad$ the length of $\mathbf r$, that is, the distance of $P$ from the origin $O$, denoted by $r$.

- $(2): \quad$ the angle between $\mathbf r$ and the polar axis, known as the colatitude of $P$, denoted by $\theta$

- $(3): \quad$ the angle between the horizontal axis and the projection of $\mathbf r$ onto the horizontal plane, known as the longitude of $P$, denoted by $\phi$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### C

### L

## Pages in category "Definitions/Spherical Coordinates"

The following 12 pages are in this category, out of 12 total.

### S

- Definition:Spherical Coordinate System
- Definition:Spherical Coordinate System/Also known as
- Definition:Spherical Coordinate System/Horizontal Axis
- Definition:Spherical Coordinate System/Initial Meridian Plane
- Definition:Spherical Coordinate System/Polar Axis
- Definition:Spherical Coordinates
- Definition:Spherical Polar Coordinates