tan1

Tan1 denotes the value of the tangent function evaluated at the input 1. In mathematics, the tangent function tan x is defined as the ratio of sine to cosine, tan x = sin x / cos x. By convention the argument 1 is taken in radians unless a different unit is specified. For x = 1 (radians), tan(1) ≈ 1.55740772465.

If the input is measured in degrees, tan(1 degree) ≈ 0.01745506493.

Tan x is defined for all x where cos x ≠ 0; its graph has vertical asymptotes at x = π/2 + kπ, where k is an integer. The Maclaurin series expansion tan x = x + x^3/3 + 2x^5/15 + 17x^7/315 + ... provides a local approximation near 0 and is useful for small-angle calculations.

In practical use, tan1—and tan values in general—appear in solving problems involving right triangles, as well as in broader trigonometric calculations, physics, engineering, and computer science. The value of tan1 is a specific instance of evaluating a trigonometric function at a fixed argument and is commonly encountered in numerical methods and scientific computations that require precise trigonometric results.