Definition:Conjugate Angles
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Definition
The conjugate of an angle $\theta$ is the angle $\phi$ such that:
- $\theta + \phi = 2 \pi$
where $\theta$ and $\pi$ are expressed in radians.
That is, it is the angle that makes the given angle equal to a full angle.
Equivalently, the conjugate of an angle $\theta$ is the angle $\phi$ such that:
- $\theta + \phi = 360 \degrees$
where $\theta$ and $\pi$ are expressed in degrees.
Thus, conjugate angles are two angles whose measures add up to the measure of $4$ right angles.
That is, their measurements add up to $360$ degrees or $2 \pi$ radians.
Also known as
The angle $2 \pi - \theta$ is also known as the explement or explementary angle of (or for, or to) $\theta$.
Also see
- Results about conjugate angles can be found here.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): conjugate: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): conjugate angles
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): conjugate angles
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): conjugate angles