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Trigonometry

Constants

SymbolValue
Degrees\frac{\pi}{180} = 0.017453292519943295769236907\ldots
Pi\pi \approx 3.14159265358979323\ldots

Trigonometric Functions

FunctionInverseHyperbolicArea Hyperbolic
SinArcsinSinhArsinh
CosArccosCoshArcosh
TanArctan
Arctan2
TanhArtanh
CotAcotCothArcoth
SecAsecSechAsech
CscAcscCschAcsch
Function
FromPolarCoordinatesConverts (\operatorname{radius}, \operatorname{angle}) \longrightarrow (x, y)
ToPolarCoordinatesConverts (x, y) \longrightarrow (\operatorname{radius}, \operatorname{angle})
Hypot\operatorname{Hypot}(x,y) = \sqrt{x^2+y^2}
Haversine\operatorname{Haversine}(z) = \sin(\frac{z}{2})^2
The Haversine function was important in navigation because it appears in the haversine formula, which is used to reasonably accurately compute distances on an astronomic spheroid given angular positions (e.g., longitude and latitude).
InverseHaversine\operatorname{InverseHaversine}(z) = 2 \operatorname{Arcsin}(\sqrt{z})