Polar sine information

In geometry, the polar sine generalizes the sine function of angle to the vertex angle of a polytope. It is denoted by psin. Let v1, ..., vn (n ≥ 1) be...

and special relativity. The basic hyperbolic functions are: hyperbolic sine "sinh" (/ˈsɪŋ, ˈsɪntʃ, ˈʃaɪn/), hyperbolic cosine "cosh" (/ˈkɒʃ, ˈkoʊʃ/)...

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to...

In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle:...

functions List of periodic functions List of trigonometric identities Polar sine – a generalization to vertex angles Proofs of trigonometric identities...

is related to the sum of the face angles, or other metrics such as the polar sine. The simplest type of polyhedral angle is a trihedral angle or trihedron...

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference...

triple product and the product of the three vector norms is known as a polar sine: a ⋅ ( b × c ) ‖ a ‖ ‖ b ‖ ‖ c ‖ = psin ⁡ ( a , b , c ) {\displaystyle...

constants Generalized trigonometry Gudermannian function Lissajous curve Polar sine Rational trigonometry Spread polynomials Abbe error Hypot Prosthaphaeresis...

Asymptotes Circular functions Periodic functions Law of cosines Law of sines Polar sine Amplitude Dot product Norm (mathematics) (also known as magnitude)...

first of the sine rules. See curved variations of the law of sines to see details of this derivation. Applying the cosine rules to the polar triangle gives...

Pythagorean theorem for a tetrahedron with a cube corner A law of sines for tetrahedra Polar sine Trigonometric functions can be defined for fractional differential...

}}y<0\end{cases}}\end{aligned}}} in the other. The arcsine function is the inverse of the sine function, and is assumed to return an angle in the range [−π/2, +π/2] = [−90°...

u_{2})+i\sin(2\pi u_{2})\right].} In contrast, the polar method here removes the need to calculate a cosine and sine. Instead, by solving for a point on the unit...

trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze...

distance from the Equator increases. Their length can be calculated by a common sine or cosine function. For example, the 60th parallel north or south is half...

lagging current represents a time shift between the current and voltage sine curves, which is represented by the angle by which the curve is ahead or...

identities for the sine and cosine function.) In other words, the absolute values are multiplied and the arguments are added to yield the polar form of the product...

by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols sl and...

× polar vector = polar vector or symbolically polar × polar = axial axial × axial = axial polar × axial = polar axial × polar = polar Because the cross...

right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle." This treatise later had a "strong...

\theta }},} where θ is the angle ∠P1P2P3. This formula uses the law of sines. If the three points are given by their coordinates (x1,y1), (x2,y2), and...