Definition:Polar Coordinates/Angular Coordinate

Definition

Let $P$ be a point in a system of polar coordinates where $O$ is the pole.

The angle measured anticlockwise from the polar axis to $OP$ is called the angular coordinate of $P$, and usually labelled $\theta$.

If the angle is measured clockwise from the polar axis to $OP$, its value is considered negative.

Also known as

The angular coordinate in a system of polar coordinates is also known as the polar angle, or azimuth.

Other words that can be seen to mean the same thing are:

• amplitude
• anomaly
• vectorial angle
• inclination.

Beware the term azimuth, as it is used in astronomy in a similar but significantly different way, to mean the angle measured clockwise from north.

Sometimes south is used.

Also see

• Definition:Radial Coordinate

• Definition:Azimuth (Astronomy)

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $2$. Coordinates
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): azimuth: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): azimuth: 1.