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The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

The tangent function is defined by tanx=(sinx)/(cosx), (1) where sinx is the sine function and cosx is the cosine function. The notation tgx is sometimes also used ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

The inverse hyperbolic secant sech^(-1)z (Beyer 1987, p. 181; Zwillinger 1995, p. 481), sometimes called the area hyperbolic secant (Harris and Stocker 1998, p. 271) and ...

Trigonometry

Formulas expressing trigonometric functions of an angle 2x in terms of functions of an angle x, sin(2x) = 2sinxcosx (1) cos(2x) = cos^2x-sin^2x (2) = 2cos^2x-1 (3) = ...

x^(2n)+1=[x^2-2xcos(pi/(2n))+1] ×[x^2-2xcos((3pi)/(2n))+1]×...× ×[x^2-2xcos(((2n-1)pi)/(2n))+1].

The Werner formulas are the trigonometric product formulas 2sinalphacosbeta = sin(alpha-beta)+sin(alpha+beta) (1) 2cosalphacosbeta = cos(alpha-beta)+cos(alpha+beta) (2) ...

Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy (ace)/(bdf)=1 (Honsberger 1995).