(trigonometry) In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg, or ctn
Used in a Sentence
cotangent
Definition, parts of speech, synonyms, and sentence examples for cotangent.
Editorial note
There, the theory is built upon vectors and covectors (i.e., differential forms) that are associated with tangent spaces and cotangent spaces, respectively.
Examples14
Definitions1
Parts of speech1
Quick take
(trigonometry) In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg, or ctn
Meaning at a glance
The clearest senses and uses of cotangent gathered in one view.
Definitions
Core meanings and parts of speech for cotangent.
noun
(trigonometry) In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg, or ctn
Example sentences
There, the theory is built upon vectors and covectors (i.e., differential forms) that are associated with tangent spaces and cotangent spaces, respectively.
What do you mean you don't know what a section of a tensor power of the cotangent bundle of a smooth Riemannian manifold means?
For me, it's the very basics of general relativity which made the distinction between the cotangent and tangents space click.
A 1-form is a section[1] of the cotangent bundle[2] of a manifold.
I have found that the biggest gap is actually understanding what sine, cosine, tangent, secant, cosecant and cotangent are.
The length of the segment from C to the origin will be the cosecant and the segment from the y axis to C will be the cotangent.
Is he suggesting that there should be a different connection (i.e., not the Levi-Civita one) on the cotangent bundle of spacetime or is it something more pedestrian?
Cotangents for structural matrices in reverse-mode AD tend to wander away from the cotangent space at the corresponding point into the tangent space of the embedding for various reasons.
Similar things happened when I sat down to understand exactly what sine, cosine, tangent, cotangent, secant and cosecant were on a circle.
In the course of it, I also managed to make very precise the notion that reverse-mode AD and pullbacks of cotangent vectors are the same thing.
At any given point p on an n -dimensional manifold, a 1-form defines an n -dimensional cotangent vector (in the language of bundles[3], a point in the fiber over p ).
Trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent are used to calculate the values of angles and sides of triangles.
Quote examples
What reverse mode AD talks informally about as "gradients" are cotangents, and if you are constrained to a submanifold of another manifold (such as the space of all symmetric matrices, embedded in the space of all NxN matrices) then your cotangent is a projection of that in the larger space.
I know it's a side point, but I loved the comment: "...explaining for instance why in any trigonometric identity such as sin(x+y) = sin(x) cos(y) + cos(x) sin(y) the number of odd functions (sine, tangent, cotangent, and their inverses) in each term has the same parity." I never thought of it that way.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use cotangent in a sentence?
There, the theory is built upon vectors and covectors (i.e., differential forms) that are associated with tangent spaces and cotangent spaces, respectively.
What does cotangent mean?
(trigonometry) In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg, or ctn
What part of speech is cotangent?
cotangent is commonly used as noun.