Pythagorean trigonometric identity information

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

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

between sine and cosine is sometimes called the fundamental Pythagorean trigonometric identity. In similar triangles, the ratios of the sides are the same...

basic relationship between the sine and the cosine is the Pythagorean trigonometric identity: cos 2 ⁡ ( θ ) + sin 2 ⁡ ( θ ) = 1 {\displaystyle \cos ^{2}(\theta...

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

before the nineteenth century Pythagorean theorem Pythagorean triple Pythagorean prime Pythagorean trigonometric identity Table of Pythagoras, another...

widely used in the study of dynamical systems. Angle measure Pythagorean trigonometric identity Riemannian circle Radian Unit disk Unit sphere Unit hyperbola...

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

^{2}x&=1\end{aligned}}} the last of which is similar to the Pythagorean trigonometric identity. One also has sech 2 ⁡ x = 1 − tanh 2 ⁡ x csch 2 ⁡ x = coth...

sides, expanding the squared binomial, and then applying the Pythagorean trigonometric identity cos 2 ⁡ γ + sin 2 ⁡ γ = 1 , {\displaystyle \cos ^{2}\gamma...

}-45^{\circ })=\sin(45^{\circ })} . Substituting into the Pythagorean trigonometric identity sin ⁡ ( 45 ∘ ) 2 + cos ⁡ ( 45 ∘ ) 2 = 1 {\displaystyle \sin(45^{\circ...

Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic...

expression involving a radical function is replaced with a trigonometric one. Trigonometric identities may help simplify the answer. Like other methods of integration...

(antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals...

square Pythagorean prime – a prime number of the form 4n + 1 Pythagorean trigonometric identity – any of several trigonometric identities Pythagorean means...

mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential...

are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation...

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

trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions...

_{1})=\operatorname {sinc} (\theta )~I.} The analog of the Pythagorean trigonometric identity holds: sin 2 ⁡ X + cos 2 ⁡ X = I {\displaystyle \sin ^{2}X+\cos...

Nonhypotenuse number Plimpton 322 Pythagorean prime Pythagorean quadruple Quadric Tangent half-angle formula Trigonometric identity Long (1972, p. 48) 1634–1699:...

\right\|^{2}\left(1-\cos ^{2}\theta \right).} Invoking the Pythagorean trigonometric identity one obtains: ‖ a × b ‖ = ‖ a ‖ ‖ b ‖ | sin ⁡ θ | , {\displaystyle...

can be implicitized in terms of x and y by way of the Pythagorean trigonometric identity. With x a = cos ⁡ ( t ) y a = sin ⁡ ( t ) {\displaystyle...

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

\right\|\left\|\mathbf {B} \right\|}}\quad (-\pi <\theta \leq \pi )} The Pythagorean trigonometric identity then provides: ‖ A × B ‖ 2 + ( A ⋅ B ) 2 = ‖ A ‖ 2 ‖ B ‖ 2...

quickly. It used the identities for the trigonometric functions of sums and differences of angles in terms of the products of trigonometric functions of those...