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:...

mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing the...

mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions...

sine wave of arbitrary phase can be written as the linear combination of two sine waves with phases of zero and a quarter cycle, the sine and cosine components...

In mathematics, particularly the field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph...

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

ordinary sine integral by Si ⁡ ( i x ) = i Shi ⁡ ( x ) . {\displaystyle \operatorname {Si} (ix)=i\operatorname {Shi} (x).} The hyperbolic cosine integral...

trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles...

versus (flipped sine), versinus, versus, or sagitta (arrow). Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine...

and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus...

expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century in Kerala, India by the mathematician and astronomer Madhava...

terms of sines and cosines, corresponding complex functions are considered of which the real parts are the original quantities. For a sine wave of a...

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 because...

of the sine function is written sin′(a) = cos(a), meaning that the rate of change of sin(x) at a particular angle x = a is given by the cosine of that...

Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written...

trigonometric function, and then simplifying the resulting integral with a trigonometric identity. The basic relationship between the sine and cosine is given by...

sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is sin 2 ⁡ θ + cos 2 ⁡ θ = 1. {\displaystyle...

and μέτρον metron, "measure". The modern words "sine" and "cosine" are derived from the Latin word sinus via mistranslation from Arabic (see Sine and...

Gaussian function. Joseph Fourier introduced sine and cosine transforms (which correspond to the imaginary and real components of the modern Fourier transform)...

wave, a mathematical function Sine and cosine transforms Sine quadrant Sine-Gordon equation Sinë, village in Albania Sine, Washington, a community in the...

greater and negative angles, see Trigonometric functions. Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine, or...

Fourier's sine and cosine transforms also perform even–odd decomposition by representing a function's odd part with sine waves (an odd function) and the function's...

remember trigonometric identities and the relationships between the various trigonometric functions. The sine, cosine, and tangent ratios in a right triangle...

Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of...

list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration. ∫ sinh ⁡ a x d x = 1 a cosh ⁡ a x...

0, 1, −1, 1/2, and −1/2. An angle can be constructed with a compass and straightedge if and only if its sine (or equivalently cosine) can be expressed...

{\textstyle t=\tan {\tfrac {x}{2}},} sines and cosines can be expressed as rational functions of t , {\displaystyle t,} and d x {\displaystyle dx} can be expressed...

arcs of circles and not functions of angles. Jyā and koti-jyā are closely related to the modern trigonometric functions of sine and cosine. In fact, the...

law of cosines, valid for arbitrary triangles. In a right triangle with sides a, b and hypotenuse c, trigonometry determines the sine and cosine of the...

complex numbers z such that zn = 1. Using the standard extensions of the sine and cosine functions to complex numbers, the formula is valid even when x is an...