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There are several q-analogs of the cosine function. The two natural definitions of the q-cosine defined by Koekoek and Swarttouw (1998) are given by cos_q(z) = ...

A function f(x) is said to be antiperiodic with antiperiod p if -f(x)=f(x+np) for n=1, 3, .... For example, the sine function sinx is antiperiodic with period pi (as well as ...

The Wallis formula follows from the infinite product representation of the sine sinx=xproduct_(n=1)^infty(1-(x^2)/(pi^2n^2)). (1) Taking x=pi/2 gives ...

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

The functions describing the horizontal and vertical positions of a point on a circle as a function of angle (cosine and sine) and those functions derived from them: cotx = ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

The hyperbolic functions sinhz, coshz, tanhz, cschz, sechz, cothz (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and ...