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Using the usual notations for a triangle (see the figure at the upper right), where a, b, c are the lengths of the three sides, A, B, C are the vertices opposite those three respective sides, α, β, γ are the corresponding angles at those vertices, s is the semiperimeter, that is, s = a + b + c / 2 , and r is the radius of the inscribed circle, the law of cotangents states that
Canonical coordinates are defined as a special set of coordinates on the cotangent bundle of a manifold.They are usually written as a set of (,) or (,) with the x ' s or q ' s denoting the coordinates on the underlying manifold and the p ' s denoting the conjugate momentum, which are 1-forms in the cotangent bundle at point q in the manifold.
Cot-1, COT-1, cot-1, or cot −1 may refer to: . Cot-1 DNA, used in comparative genomic hybridization; cot −1 y = cot −1 (y), sometimes interpreted as arccot(y) or arccotangent of y, the compositional inverse of the trigonometric function cotangent (see below for ambiguity)
All cotangent spaces at points on a connected manifold have the same dimension, equal to the dimension of the manifold.All the cotangent spaces of a manifold can be "glued together" (i.e. unioned and endowed with a topology) to form a new differentiable manifold of twice the dimension, the cotangent bundle of the manifold.
In mathematics, Hermite's cotangent identity is a trigonometric identity discovered by Charles Hermite. [1] Suppose a 1 , ..., a n are complex numbers , no two of which differ by an integer multiple of π .
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
The total complex of this simplicial object is the cotangent complex L B/A. The morphism r induces a morphism from the cotangent complex to Ω B / A called the augmentation map . In the homotopy category of simplicial A -algebras (or of simplicial ringed topoi), this construction amounts to taking the left derived functor of the Kähler ...
In mathematics, a function f is cofunction of a function g if f(A) = g(B) whenever A and B are complementary angles (pairs that sum to one right angle). [1] This definition typically applies to trigonometric functions. [2] [3] The prefix "co-" can be found already in Edmund Gunter's Canon triangulorum (1620). [4] [5]