supplementary angles
Two angles are called supplementary angles of each other if the sum of their measures (http://planetmath.org/AngleMeasure) is equal to the straight angle , i.e. (http://planetmath.org/Ie) .
For example, when two lines intersect each other, they the plane into four disjoint domains (http://planetmath.org/Domain2) corresponding to four convex angles; then any of these angles has a supplementary angle on either side of it (see linear pair). However, two angles that are supplementary to each other do not need to have a common side — see e.g. (http://planetmath.org/Eg) an entry regarding opposing angles in a cyclic quadrilateral (http://planetmath.org/OpposingAnglesInACyclicQuadrilateralAreSupplementary).
Supplementary angles have always equal sines, but the cosines are opposite numbers:
These formulae may be proved by using the subtraction formulas of sine and cosine.
Title | supplementary angles |
Canonical name | SupplementaryAngles |
Date of creation | 2013-03-22 17:34:59 |
Last modified on | 2013-03-22 17:34:59 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 8 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 51M04 |
Classification | msc 51F20 |
Synonym | supplementary |
Related topic | Supplement |
Related topic | Angle |
Related topic | ComplementaryAngles |
Related topic | GoniometricFormulae |