are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition...

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...

Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions...

not in the interval [0, π/2], see Proofs of trigonometric identities). For non-geometrical proofs using only tools of calculus, one may use directly the...

sine theorem Polar sine—a generalization to vertex angles Proofs of trigonometric identities Sinc function Sine and cosine transforms Sine integral Sine...

earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied...

cotangent identity Lagrange's trigonometric identities Morrie's law Proofs of trigonometric identities Pythagorean trigonometric identity Tangent half-angle...

mathematical identities are relatively simple (for an experienced mathematician), though not necessarily unimportant. The trivial logarithmic identities are as...

traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations...

divergence Theorem. Half-side formula Law of sines Law of tangents Law of cotangents List of trigonometric identities Mollweide's formula Given sides ⁠ b {\displaystyle...

theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy. If the vertices of the cyclic quadrilateral are A, B...

with exponent n means. Various proofs of the formula are possible. This proof shows that the quotient of the trigonometric and exponential expressions is...

a trigonometric way) that are equivalent to specific trigonometric laws or formulas. For instance, propositions twelve and thirteen of book two of the...

for multivariable calculus Trigonometric functions – Functions of an angle Vector calculus identities – Mathematical identities Calculus (5th edition), F...

trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric functions...

place of trigonometric functions. An advantage of Wildberger's methods noted by Henle is that, because they involve only simple algebra, the proofs are...

mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean...

Mollweide and Some Trigonometric Identities" (PDF) (preprint) Wu, Rex H. (2020), "Proof Without Words: The Mollweide Equations from the Law of Sines", Mathematics...

many identities, all of them similar in form to the trigonometric identities. In fact, Osborn's rule states that one can convert any trigonometric identity...

using trigonometry as below, or the incenter and one excircle of the triangle, or as a special case of De Gua's theorem (for the particular case of acute...

below for proofs). In the table below, the label "Undefined" represents a ratio 1 : 0. {\displaystyle 1:0.} If the codomain of the trigonometric functions...

law of sines is one of two trigonometric equations commonly applied to find lengths and angles in scalene triangles, with the other being the law of cosines...

Geometrically, trigonometric identities are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are...

divisors Table of integrals Table of mathematical symbols Table of prime factors Taylor series Timeline of mathematics Trigonometric identities Truth table...

-iər/) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing...

exercised with trigonometric functions and trigonometric identities. The binomial theorem, polar coordinates, parametric equations, and the limits of sequences...

internal angles and triangles creates a new concept of trigonometric functions. The primary trigonometric functions are sine and cosine, as well as the other...

{\text{via trigonometric identities}}\end{alignedat}}} See angle sum and difference identities. We deduce that S(k) implies S(k + 1). By the principle of mathematical...

i sin ⁡ x {\displaystyle e^{ix}=\cos x+i\sin x} where the inputs of the trigonometric functions sine and cosine are given in radians. In particular, when...

In trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle. The tangent of half...