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...

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

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...

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

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

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

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

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...

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

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

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...

logarithmic functions List of mathematical identities Lists of mathematics topics List of trigonometric identities Weisstein, Eric W. "Logarithm". mathworld...

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

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

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

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

Divergence Theorem. Half-side formula Law of sines Law of tangents Law of cotangents List of trigonometric identities Mollweide's formula Given sides b , c...

differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect...

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

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

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...

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...

Morrie's law is a special trigonometric identity. Its name is due to the physicist Richard Feynman, who used to refer to the identity under that name. Feynman...

logarithms that would supplant it. The trigonometric identities exploited by prosthaphaeresis relate products of trigonometric functions to sums. They include...

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

In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles...

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

)&=&2a(1-\cos \varphi )\cdot \sin \varphi &.&\end{array}}} (The trigonometric identities e i φ = cos ⁡ φ + i sin ⁡ φ ,   ( cos ⁡ φ ) 2 + ( sin ⁡ φ ) 2 =...