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

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

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...

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...

heat transfer, and fluid dynamics. 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...

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...

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

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

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

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

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

due to Aryabhata (sixth century AD), who discovered the sine function, cosine function, and versine function.[citation needed] During the Middle Ages...

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...

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

A}}={\frac {b}{a}}.} The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary...

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...

of the Poisson bracket), as the cosine bracket leads to the classical Hamilton–Jacobi equation. The sine and cosine bracket also stand in relation to...

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

{\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...

|\sin ax-\cos ax|+C} An integral that is a rational function of the sine and cosine can be evaluated using Bioche's rules. ∫ d x cos ⁡ a x ± sin ⁡ a x...

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

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

transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which...

internal technical report proposing the CORDIC algorithm to solve sine and cosine functions and a prototypical computer implementing it. The report also discussed...

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

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...

The trigonometric functions (especially sine and cosine) for complex square matrices occur in solutions of second-order systems of differential equations...