# Generalized trigonometry – Wikipedia

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Study of triangles in other spaces than the Euclidean plane

Ordinary trigonometry studies triangles in the Euclidean plane

${displaystyle mathbb {R} ^{2}}$. There are a number of ways of defining the ordinary Euclidean geometric trigonometric functions on real numbers, for example right-angled triangle definitions, unit circle definitions, series definitions, definitions via differential equations, and definitions using functional equations. **Generalizations of trigonometric functions** are often developed by starting with one of the above methods and adapting it to a situation other than the real numbers of Euclidean geometry. Generally, trigonometry can be the study of triples of points in any kind of geometry or space. A triangle is the polygon with the smallest number of vertices, so one direction to generalize is to study higher-dimensional analogs of angles and polygons: solid angles and polytopes such as tetrahedrons and n-simplices.

## Trigonometry[edit]

## Higher dimensions[edit]

## Trigonometric functions[edit]

## See also[edit]

## References[edit]

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