Tan5

Tan5 typically refers to the value of the tangent function at the input 5, usually understood in radians unless the context specifies degrees. In this conventional sense, tan(5) is a real number approximately equal to −3.3805.

Mathematical context

The tangent function tan(x) is defined as sin(x) divided by cos(x). It is defined for all real x except where cos(x) = 0 (at x = π/2 + kπ, where k is an integer), where tan(x) has vertical asymptotes. Tan(x) is periodic with period π, meaning tan(x + π) = tan(x). If the angle were intended in degrees, tan(5) would denote tan(5°), which equals about 0.0875.

Computational usage

In programming and scientific calculators, tan(5) is computed by taking the tangent of 5 in the current angle mode. Most languages expect radians by default for mathematical functions, so tan(5) ≈ −3.3805 in radians. In deg mode, tan(5) would yield about 0.0875.

Related considerations

The value tan(5) can be expressed as sin(5)/cos(5). The function’s graph rises from negative to positive infinity across each asymptote and exhibits the characteristic S-shape within each interval between asymptotes.

See also

Tangent function, trigonometric functions, radian measure, degree measure. The term tan is short for tangent, a fundamental trigonometric function with applications in geometry, physics, engineering, and computer science.