Coterminal Angle

Two non-coincident plane angles alpha and beta in angle standard position are said to be coterminal if the terminal side of alpha is identically the same as the terminal side of beta.

In general, given a plane angle alpha measured in radians, beta is coterminal to alpha if and only if beta=alpha+/-2npi for some positive integer n in Z^+. Similarly, if beta is a plane angle coterminal to a plane angle alpha measured in degrees, then beta=alpha+/-360n for some positive integer n in Z^+. In the event that n=0, then alpha and beta are coincident.


In the figure above, the non-coincident angles alpha=pi/4 and beta=9pi/4 are coterminal angles.

See also

Angle, Angle Standard Position, Coincident, Initial Side, Terminal Side

This entry contributed by Christopher Stover

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Cite this as:

Stover, Christopher. "Coterminal Angle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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