Trigonometry

Constants

Symbol Value
Degrees \[ \frac{\pi}{180} = 0.017453292519943295769236907\ldots \]
MinusDoublePi \[ -2\pi \]
MinusPi \[ -\pi \]
MinusHalfPi \[ -\frac{\pi}{2} \]
QuarterPi \[ \frac{\pi}{4} \]
ThirdPi \[ \frac{\pi}{3} \]
HalfPi \[ \frac{\pi}{2} \]
TwoThirdPi \[ 2\times \frac{\pi}{3} \]
ThreeQuarterPi \[ 3\times \frac{\pi}{4} \]
Pi \[ \pi \approx 3.14159265358979323\ldots \]
DoublePi \[ 2\pi \]

Trigonometric Functions

Function Inverse Hyperbolic Area Hyperbolic
Sin Arcsin Sinh Arsinh
Cos Arccos Cosh Arcosh
Tan Arctan Arctan2 Tanh Artanh
Cot Acot Coth Arcoth
Sec Asec Sech Asech
Csc Acsc Csch Acsch
Function
FromPolarCoordinates Converts \( (\operatorname{radius}, \operatorname{angle}) \longrightarrow (x, y)\)
ToPolarCoordinates Converts \((x, y) \longrightarrow (\operatorname{radius}, \operatorname{angle})\)
Hypot \(\operatorname{Hypot}(x,y) = \sqrt{x^2+y^2}\) numeric
Haversine \( \operatorname{Haversine}(z) = \sin(\frac{z}{2})^2 \) numeric
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 \(\operatorname{InverseHaversine}(z) = 2 \operatorname{Arcsin}(\sqrt{z})\) numeric