cot90

Cot90 refers to the value of the cotangent function at an angle of 90 degrees. The cotangent function is defined as cot x = cos x / sin x. At x = 90° (π/2 radians), cos 90° = 0 and sin 90° = 1, so cot 90° = 0. This makes 90° a zero of the cotangent function. By contrast, tan 90° is undefined because it involves division by zero (cos 90° = 0).

Cotangent can also be viewed as the reciprocal of tangent: cot x = 1 / tan x, for angles where tan x ≠ 0. In a right triangle, cot(θ) equals the ratio of the adjacent leg to the opposite leg. More generally, cot x is the ratio cos x to sin x, and it is undefined whenever sin x = 0 (that is, at x = kπ, where k is an integer).

The graph of cot x has period π and features vertical asymptotes where sin x = 0 (at x = kπ) and zeros where cos x = 0 with sin x ≠ 0 (at x = π/2 + kπ). In degree measure, its zeros occur at 90°, 270°, etc., and its asymptotes at 0°, 180°, 360°, etc.

Cot90° is thus a simple example illustrating that the cotangent of 90 degrees equals zero, while the tangent is undefined at that angle. This distinction reflects the broader properties and domain of the cotangent function.