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Longer titles found: Sine and cosine transforms (view), Fourier sine and cosine series (view)

searching for sine and cosine 166 found (212 total)

Pythagorean trigonometric identity (2,083 words) [view diff] exact match in snippet view article find links to article

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

Pure tone (615 words) [view diff] exact match in snippet view article find links to article

amplitude change between such a system's pure-tone input and its output. Sine and cosine waves can be used as basic building blocks of more complex waves. As

Empirical orthogonal functions (343 words) [view diff] exact match in snippet view article find links to article

analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies. In some cases the two methods may yield

List of integrals of hyperbolic functions (2,004 words) [view diff] no match in snippet view article find links to article

The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals

Sine wave (1,332 words) [view diff] exact match in snippet view article find links to article

combination of two sine waves with phases of zero and a quarter cycle, the sine and cosine components, respectively. Sine wave Five seconds of a 220 Hz sine wave

Golden angle (692 words) [view diff] exact match in snippet view article find links to article

follow from well-known algebraic properties of the golden ratio. As its sine and cosine are transcendental numbers, the golden angle cannot be constructed

Madhava series (4,624 words) [view diff] exact match in snippet view article find links to article

later independently discovered in 17th century Europe. The series for sine and cosine were rediscovered by Isaac Newton in 1669, and the series for arctangent

Yuktibhāṣā (1,996 words) [view diff] exact match in snippet view article find links to article

Taylor series, including second and third order approximations of sine and cosine; radii, diameters and circumferences. Yuktibhāṣā mainly gives rationale

Tangent half-angle substitution (3,042 words) [view diff] exact match in snippet view article find links to article

ISBN 978-1-108-41881-2. Other trigonometric functions can be written in terms of sine and cosine. Gunter, Edmund (1673) [1624]. The Works of Edmund Gunter. Francis

Timeline of geometry (1,413 words) [view diff] exact match in snippet view article find links to article

numerical values. It defines the concepts of sine and cosine, and also contains the earliest tables of sine and cosine values (in 3.75-degree intervals from

Transcendental function (1,945 words) [view diff] exact match in snippet view article find links to article

functions sine and cosine by introducing (−1)k into the series, resulting in alternating series. After Euler, mathematicians view the sine and cosine this

Simple cell (912 words) [view diff] exact match in snippet view article find links to article

when seeing an isolated bar. Using the mathematical Gabor model with sine and cosine components (phases), complex cells are then modeled by computing the

Trigonometric functions of matrices (601 words) [view diff] exact match in snippet view article find links to article

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

Resolver (electrical) (980 words) [view diff] exact match in snippet view article

fixed at right (90°) angles to each other on the stator, produce a sine and cosine feedback current. The relative magnitudes of the two-phase voltages

Entire function (3,277 words) [view diff] exact match in snippet view article find links to article

products and compositions of these, such as the trigonometric functions sine and cosine and their hyperbolic counterparts sinh and cosh, as well as derivatives

Euler's formula (3,851 words) [view diff] exact match in snippet view article find links to article

between analysis and trigonometry, and provides an interpretation of the sine and cosine functions as weighted sums of the exponential function: cos ⁡ x = Re

De Moivre's formula (2,449 words) [view diff] exact match in snippet view article find links to article

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

Lock-in amplifier (2,185 words) [view diff] exact match in snippet view article find links to article

by fast digital signal processing, for example, on an FPGA. Usually sine and cosine demodulation is performed simultaneously, which is sometimes also referred

Dixon elliptic functions (5,056 words) [view diff] exact match in snippet view article find links to article

{\displaystyle x^{3}+y^{3}=1} , just as the trigonometric functions sine and cosine parametrize the unit circle x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1}

Proofs of trigonometric identities (5,714 words) [view diff] exact match in snippet view article find links to article

definitions, and therefore other proofs are based on the Taylor series of sine and cosine, or on the differential equation f ″ + f = 0 {\displaystyle f''+f=0}

Periodic function (1,704 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f} is the sawtooth wave. The trigonometric functions sine and cosine are common periodic functions, with period 2 π {\displaystyle 2\pi

Indian mathematics (14,795 words) [view diff] exact match in snippet view article find links to article

further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted

Complex number (11,623 words) [view diff] exact match in snippet view article find links to article

} (These are a consequence of the trigonometric identities for the sine and cosine function.) In other words, the absolute values are multiplied and the

AP Precalculus (457 words) [view diff] case mismatch in snippet view article find links to article

Phenomena 2 3.2 Sine, Cosine, and Tangent 2 3.3 Sine and Cosine Function Values 2 3.4 Sine and Cosine Function Graphs 2 3.5 Sinusoidal Functions 2 3.6

Moyal bracket (1,359 words) [view diff] exact match in snippet view article find links to article

differentiable phase-space functions, and f g is the ordinary product. The sine and cosine brackets are, respectively, the results of antisymmetrizing and symmetrizing

Least-squares spectral analysis (3,354 words) [view diff] exact match in snippet view article find links to article

simplification in general, except for pair-wise correlations between sine and cosine bases of the same frequency, since the correlations between pairs of

1571 in science (197 words) [view diff] exact match in snippet view article find links to article

singularis containing many trigonometric tables and formulas on the sine and cosine, and novel in using a decimal notation; publication continued until

Bernoulli polynomials (4,252 words) [view diff] exact match in snippet view article find links to article

limit of large degree, they approach, when appropriately scaled, the sine and cosine functions. A similar set of polynomials, based on a generating function

Bivariate von Mises distribution (697 words) [view diff] exact match in snippet view article find links to article

commonly used variants of the bivariate von Mises distribution are the sine and cosine variant. The cosine variant of the bivariate von Mises distribution

Phase-shift keying (6,226 words) [view diff] exact match in snippet view article find links to article

frequency carrier wave. The modulation is accomplished by varying the sine and cosine inputs at a precise time. It is widely used for wireless LANs, RFID

A History of the Kerala School of Hindu Astronomy (711 words) [view diff] exact match in snippet view article find links to article

Newton-Gauss interpolation formula, Taylor series for sine and cosine functions, power series for sine and cosine functions, Lhuier's formula for the circum-radius

Unit interval (759 words) [view diff] exact match in snippet view article find links to article

occurs frequently, such as in the range of the trigonometric functions sine and cosine and the hyperbolic function tanh. This interval may be used for the

Kerala school of astronomy and mathematics (3,516 words) [view diff] exact match in snippet view article find links to article

given in two papers, a commentary on the Yuktibhasa's proof of the sine and cosine series and two papers that provide the Sanskrit verses of the Tantrasangrahavakhya

Cadambathur Tiruvenkatacharlu Rajagopal (510 words) [view diff] exact match in snippet view article find links to article

Scripta Mathematica 17: 65–74. 1949: (with A. Venkataraman) "The sine and cosine power series in Hindu mathematics", Journal of the Royal Asiatic Society

Euler's identity (1,963 words) [view diff] exact match in snippet view article find links to article

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

Linear encoder (1,612 words) [view diff] exact match in snippet view article find links to article

outputs. The industry standard analog output for linear encoders is sine and cosine quadrature signals. These are usually transmitted differentially so

Karanapaddhati (1,362 words) [view diff] exact match in snippet view article find links to article

The following verse describes the infinite series expansions of the sine and cosine functions. cāpācca tattat phalato'pi tadvat cāpāhatāddvayādihatat

Lemniscate elliptic functions (23,108 words) [view diff] exact match in snippet view article find links to article

lemn are used instead), are analogous to the trigonometric functions sine and cosine. While the trigonometric sine relates the arc length to the chord length

Circular uniform distribution (952 words) [view diff] exact match in snippet view article find links to article

{S}}={\overline {R}}e^{i{\overline {\theta }}}} where the average sine and cosine are: C ¯ = 1 N ∑ n = 1 N cos ⁡ ( θ n ) S ¯ = 1 N ∑ n = 1 N sin ⁡ (

Holonomic function (1,977 words) [view diff] exact match in snippet view article find links to article

rational functions the sine and cosine functions (but not tangent, cotangent, secant, or cosecant) the hyperbolic sine and cosine functions (but not hyperbolic

Kriyakramakari (1,126 words) [view diff] case mismatch in snippet view article find links to article

of the odd ones, [that] should be the arc. Here, the smaller of the Sine and Cosine is required to be considered as the desired [Sine]. Otherwise there

Curve fitting (2,139 words) [view diff] exact match in snippet view article find links to article

acceptable. Other types of curves, such as trigonometric functions (such as sine and cosine), may also be used, in certain cases. In spectroscopy, data may be

Unit circle (1,009 words) [view diff] exact match in snippet view article find links to article

^{2}\theta +\sin ^{2}\theta =1.} The unit circle also demonstrates that sine and cosine are periodic functions, with the identities cos ⁡ θ = cos ⁡ ( 2 π k

Law of cosines (5,707 words) [view diff] exact match in snippet view article find links to article

of rectangle areas; Hellenistic trigonometry developed later, and sine and cosine per se first appeared centuries afterward in India. The cases of obtuse

Exponential integral (2,995 words) [view diff] no match in snippet view article find links to article

retrieved 2011-08-09 Temme, N. M. (2010), "Exponential, Logarithmic, Sine, and Cosine Integrals", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald

All Alone (Dolo Coker album) (152 words) [view diff] case mismatch in snippet view article

compositions by Dolo Coker except as indicated "Reflections" - 5:54 "Sine and Cosine" - 2:15 "Just You" - 4:36 "Cabin in the Sky" (Vernon Duke, John La

Eccentric anomaly (1,148 words) [view diff] exact match in snippet view article find links to article

anomaly are related as follows. Using the formula for r above, the sine and cosine of E are found in terms of f : cos ⁡ E = x a = a e + r cos ⁡ f a =

Hardy field (925 words) [view diff] exact match in snippet view article find links to article

multiplicative inverse or are zero. This means periodic functions such as the sine and cosine functions cannot exist in Hardy fields. This avoidance of periodic

Air core gauge (438 words) [view diff] exact match in snippet view article find links to article

{x}{y}}\right)} Where x {\displaystyle x} and y {\displaystyle y} are the coils' sine and cosine currents respectively. The permanent magnet aligns itself with that

Integration using Euler's formula (1,135 words) [view diff] exact match in snippet view article find links to article

function and sine is odd. These two equations can be solved for the sine and cosine to give cos ⁡ x = e i x + e − i x 2 and sin ⁡ x = e i x − e − i x 2

Logarithmic integral function (1,104 words) [view diff] no match in snippet view article find links to article

MR 0167642. LCCN 65-12253. Temme, N. M. (2010), "Exponential, Logarithmic, Sine, and Cosine Integrals", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald

Timeline of mathematics (7,788 words) [view diff] exact match in snippet view article find links to article

numerical values. It defines the concepts of sine and cosine, and also contains the earliest tables of sine and cosine values (in 3.75-degree intervals from

Exponential function (5,755 words) [view diff] exact match in snippet view article find links to article

that, restricted to real arguments, the sine and cosine functions as defined above coincide with the sine and cosine functions as introduced in elementary

Almost periodic function (2,838 words) [view diff] exact match in snippet view article find links to article

linear combination of sine and cosine waves that is of distance less than ε from f with respect to the uniform norm. The sine and cosine frequencies can be

Square and Compass, Worth Matravers (967 words) [view diff] case mismatch in snippet view article find links to article

Research Establishment scientists in Purbeck, who knew the inn as Sine and Cosine. The public house includes a small museum which displays fossils and

Cofunction (335 words) [view diff] exact match in snippet view article find links to article

Sine and cosine are each other's cofunctions.

Ganita Kaumudi (1,160 words) [view diff] exact match in snippet view article find links to article

generalization here was crucial for finding the infinite series for sine and cosine. 28 rules and 19 examples. Geometry. 149 rules and 94 examples. Includes

Lawrence Crawford (mathematician) (343 words) [view diff] case mismatch in snippet view article

They had three sons and two daughters. On the Use of the Hyperbolic Sine and Cosine (1895) The Tides (1897) The Trisection of a Given Angle (1898) Evaluation

Bounded function (985 words) [view diff] case mismatch in snippet view article find links to article

and Scientists, 5th Edition. CRC Press. ISBN 978-0-412-62150-5. "The Sine and Cosine Functions" (PDF). math.dartmouth.edu. Archived (PDF) from the original

Alternating series (1,693 words) [view diff] exact match in snippet view article find links to article

_{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}x^{n}\;=\;\ln(1+x).} The functions sine and cosine used in trigonometry and introduced in elementary algebra as the ratio

Quaternions and spatial rotation (11,558 words) [view diff] exact match in snippet view article find links to article

intuitive and easy to understand and, due to the periodic nature of sine and cosine, rotation angles differing precisely by the natural period will be

Bhāskara I (1,346 words) [view diff] exact match in snippet view article find links to article

0 {\displaystyle x=0} ). Additionally, he gives relations between sine and cosine, as well as relations between the sine of an angle less than 90° and

Mathematical table (1,458 words) [view diff] exact match in snippet view article find links to article

culminating in the discovery of the power series expansions of the sine and cosine functions by Madhava of Sangamagrama (c.1350 – c.1425), and the tabulation

Supertoroid (810 words) [view diff] exact match in snippet view article find links to article

similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u

Kosambi–Karhunen–Loève theorem (10,711 words) [view diff] exact match in snippet view article find links to article

and the expansion basis consists of sinusoidal functions (that is, sine and cosine functions), the coefficients in the Karhunen–Loève theorem are random

Lemniscate of Bernoulli (1,199 words) [view diff] exact match in snippet view article find links to article

The lemniscate sine and cosine relate the arc length of an arc of the lemniscate to the distance of one endpoint from the origin.

Complex harmonic motion (963 words) [view diff] exact match in snippet view article find links to article

similarly to the simple pendulum because the motion is determined by sine and cosine functions as well. The image shows a marine clock with motor springs

Vincenzo Riccati (1,296 words) [view diff] exact match in snippet view article find links to article

modern publications, and formulated the addition laws of hyperbolic sine and cosine: C A = r , C B = C h . φ , B E = S h . φ , C D = C h . π ,

Stumpff function (674 words) [view diff] exact match in snippet view article find links to article

{-x\ }}}~.\end{aligned}}} Circular orbits and elliptical orbits use sine and cosine relations, and hyperbolic orbits use the sinh and cosh relations. Parabolic

FPS AP-120B (898 words) [view diff] exact match in snippet view article find links to article

the hardware was delivered with a pre-calculated lookup table of sine and cosine values. Sines and cosines for angles from 0 to π/2 radians were stored

Murderous Maths (1,865 words) [view diff] exact match in snippet view article find links to article

right angled triangles, trig on a calculator; normal and inverse, sine and cosine formulas for non-right-angled triangles, triangulation, parallax angles

Marsaglia polar method (1,410 words) [view diff] exact match in snippet view article find links to article

{-2\ln(u_{1})}},} but that transform requires logarithm, square root, sine and cosine functions. On some processors, the cosine and sine of the same argument

Analog computer (6,932 words) [view diff] exact match in snippet view article find links to article

that pin was a square block. Rectilinear-coordinate outputs (both sine and cosine, typically) came from two slotted plates, each slot fitting on the

Area of a circle (5,880 words) [view diff] exact match in snippet view article find links to article

r^{2}} . This particular proof may appear to beg the question, if the sine and cosine functions involved in the trigonometric substitution are regarded as

Pythagorean theorem (12,566 words) [view diff] exact match in snippet view article find links to article

triangle with sides a, b and hypotenuse c, trigonometry determines the sine and cosine of the angle θ between side a and the hypotenuse as: sin ⁡ θ = b c

Euler angles (5,214 words) [view diff] exact match in snippet view article find links to article

=\arcsin \left(Y_{3}/{\sqrt {1-X_{3}^{2}}}\right).} Note that the inverse sine and cosine functions yield two possible values for the argument. In this geometrical

Euler–Rodrigues formula (2,056 words) [view diff] exact match in snippet view article find links to article

φ is increased by a full rotation of 360 degrees, the arguments of sine and cosine only increase by 180 degrees. The resulting parameters are the opposite

Damping (2,749 words) [view diff] exact match in snippet view article find links to article

given sinusoidal waveform may be of intermediate phase, having both sine and cosine components. The term "damped sine wave" describes all such damped waveforms

Weierstrass factorization theorem (1,872 words) [view diff] exact match in snippet view article find links to article

}E_{p_{n}}\!\!\left({\frac {z}{a_{n}}}\right).} The trigonometric functions sine and cosine have the factorizations sin ⁡ π z = π z ∏ n ≠ 0 ( 1 − z n ) e z / n

Collatz conjecture (7,090 words) [view diff] exact match in snippet view article find links to article

to the complex plane. They used Chamberland's function for complex sine and cosine and added the extra term 1 π ( 1 2 − cos ⁡ ( π z ) ) sin ⁡ ( π z )

Prosthaphaeresis (1,972 words) [view diff] exact match in snippet view article find links to article

prosthaphaeresis with values for every second, or 3600th of a degree. Inverse sine and cosine functions are particularly troublesome, because they become steep near

Helmholtz equation (2,973 words) [view diff] exact match in snippet view article find links to article

equation in time. The solution in time will be a linear combination of sine and cosine functions, whose exact form is determined by initial conditions, while

RC oscillator (1,957 words) [view diff] exact match in snippet view article find links to article

It is possible to stabilize a quadrature oscillator by squaring the sine and cosine outputs, adding them together, (Pythagorean trigonometric identity)

Integration by substitution (3,322 words) [view diff] exact match in snippet view article find links to article

be integrated using substitution by expressing it in terms of the sine and cosine: tan ⁡ x = sin ⁡ x cos ⁡ x {\displaystyle \tan x={\tfrac {\sin x}{\cos

Evoked potential (5,213 words) [view diff] exact match in snippet view article find links to article

flickering (sinusoidally modulated) light. Rather than integrating the sine and cosine products, Regan fed the signals to a two-pen recorder via lowpass filters

Cauchy sequence (3,219 words) [view diff] exact match in snippet view article find links to article

Golden ratio, which is irrational. The values of the exponential, sine and cosine functions, exp(x), sin(x), cos(x), are known to be irrational for any

Spring (device) (3,353 words) [view diff] exact match in snippet view article

{d^{2}x}{dt^{2}}}+{\frac {k}{m}}x=0,\,} the solution of which is the sum of a sine and cosine: x ( t ) = A sin ⁡ ( t k m ) + B cos ⁡ ( t k m ) . {\displaystyle x(t)=A\sin

Rotary encoder (2,819 words) [view diff] exact match in snippet view article find links to article

sine encoders, which output sinusoidal waveforms in quadrature (i.e., sine and cosine), thus combining the characteristics of an encoder and a resolver.

Lissajous-toric knot (933 words) [view diff] exact match in snippet view article find links to article

Lissajous-toric knot onto the x-y-plane is a Lissajous curve. Replacing the sine and cosine functions in the parametrization by a triangle wave transforms a Lissajous-toric

Lookup table (3,070 words) [view diff] exact match in snippet view article find links to article

floating-point divide bug. Functions of a single variable (such as sine and cosine) may be implemented by a simple array. Functions involving two or more

List of common coordinate transformations (2,162 words) [view diff] exact match in snippet view article find links to article

In this case in all formulas below all arguments in θ should have sine and cosine exchanged, and as derivative also a plus and minus exchanged. All divisions

Rangekeeper (4,719 words) [view diff] exact match in snippet view article find links to article

computer multipliers were based on the geometry of similar triangles. Sine and cosine generation (polar-to-rectangular coordinate conversion) These mechanisms

Peskin–Takeuchi parameter (1,801 words) [view diff] exact match in snippet view article find links to article

}(0)-s_{w}^{2}\Pi _{\gamma \gamma }^{\prime }(0)\right]} where sw and cw are the sine and cosine of the weak mixing angle, respectively. The definitions are carefully

History of mathematics (16,142 words) [view diff] exact match in snippet view article find links to article

the Madhava-Newton power series to determine sine and cosine and the Taylor approximation for sine and cosine functions. In the 16th century, Jyesthadeva

Box–Muller transform (2,089 words) [view diff] exact match in snippet view article find links to article

R2, which is likewise uniformly distributed. The definitions of the sine and cosine are then applied to the basic form of the Box–Muller transform to avoid

Interval arithmetic (8,154 words) [view diff] exact match in snippet view article find links to article

where the monotonicity of the function changes direction. For the sine and cosine functions, the critical points are at ( 1 2 + n ) π {\displaystyle

Aryabhata (4,786 words) [view diff] no match in snippet view article find links to article

90°, to an accuracy of 4 decimal places. In fact, the modern terms "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by

Line (geometry) (4,301 words) [view diff] exact match in snippet view article

be proven geometrically by applying right triangle definitions of sine and cosine to the right triangle that has a point of the line and the origin as

Equation (4,237 words) [view diff] exact match in snippet view article find links to article

manipulating or solving trigonometric equations. Two of many that involve the sine and cosine functions are: sin 2 ⁡ ( θ ) + cos 2 ⁡ ( θ ) = 1 {\displaystyle \sin

Modulation (3,050 words) [view diff] exact match in snippet view article find links to article

component. Carry out the modulation, for example by multiplying the sine and cosine waveform with the I and Q signals, resulting in the equivalent low

Logarithm (11,600 words) [view diff] exact match in snippet view article find links to article

r={\sqrt {x^{2}+y^{2}}}.} Using the geometrical interpretation of sine and cosine and their periodicity in 2π, any complex number z may be denoted as

Theorem (4,394 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \tan(\alpha +\beta )} from the addition formulas of sine and cosine. Petkovsek et al. 1996. Wentworth, G.; Smith, D.E. (1913). Plane Geometry

AN/FSQ-7 Combat Direction Central (2,372 words) [view diff] exact match in snippet view article find links to article

register which was incremented 32 times a second.: 27 Trigonometric sine and cosine functions used 1.4 degree precision (256 values) via look-up tables

Trigonometric integral (3,230 words) [view diff] no match in snippet view article find links to article

Differential Equations. Temme, N.M. (2010), "Exponential, Logarithmic, Sine, and Cosine Integrals", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald

Wheel speed sensor (2,793 words) [view diff] exact match in snippet view article find links to article

magneto-resistive sensor scans a target wheel with 256 teeth, generating sine and cosine signals. Arctangent interpolation is used to generate rectangular pulses

Seasonality (2,502 words) [view diff] exact match in snippet view article find links to article

sinusoidal model, Fourier terms added into regression models utilize sine and cosine terms in order to simulate seasonality. However, the seasonality of

Trend periodic nonstationary processes (966 words) [view diff] exact match in snippet view article find links to article

periodic stationary processes is by using a regression model with a sine and cosine function, such as: x ( t ) = β 0 + β 1 t + β 2 c o s ( 2 π t / T )

Madhava of Sangamagrama (3,711 words) [view diff] exact match in snippet view article find links to article

unknown Sanskrit work concerning Madhava's derivation of the power series for sine and cosine", Historia Scientiarum, 42: 49–65. Biography on MacTutor

Eclipse cycle (10,441 words) [view diff] exact match in snippet view article find links to article

and distance of the Moon and of the Sun using sine and cosine series. The arguments of the sine and cosine functions depend on only four values, the Delaunay

Glossary of electrical and electronics engineering (19,294 words) [view diff] exact match in snippet view article find links to article

mathematical technique for representing a sampled signal as a sum of sine and cosine waves of different frequencies. discrete-time signal A signal represented

Vibrations of a circular membrane (2,508 words) [view diff] exact match in snippet view article find links to article

convenience. Then, T ( t ) {\displaystyle T(t)} is a linear combination of sine and cosine functions, T ( t ) = A cos ⁡ c λ t + B sin ⁡ c λ t . {\displaystyle

Bicentric quadrilateral (3,735 words) [view diff] exact match in snippet view article find links to article

{cd}{ab}}}=\cot {\frac {D}{2}}.\end{aligned}}} Using the same notations, for the sine and cosine functions the following formulas holds: sin ⁡ A 2 = b c a d + b c =

Circle (6,119 words) [view diff] exact match in snippet view article find links to article

can be written in parametric form using the trigonometric functions sine and cosine as x = a + r cos ⁡ t , y = b + r sin ⁡ t , {\displaystyle {\begin{aligned}x&=a+r\

Single-sideband modulation (4,797 words) [view diff] exact match in snippet view article find links to article

the middle of the voiceband, but implemented by a quadrature pair of sine and cosine modulators at that frequency (e.g. 2 kHz). This complex signal or pair

Radian (5,387 words) [view diff] exact match in snippet view article find links to article

angles are involved, mathematically important relationships between the sine and cosine functions and the exponential function (see, for example, Euler's formula)

Squigonometry (1,107 words) [view diff] exact match in snippet view article find links to article

corresponds to s q p ( t ) {\displaystyle sq_{p}(t)} . The definition of sine and cosine through integrals can be extended to define the squigonometric functions

Underwater acoustic communication (1,927 words) [view diff] exact match in snippet view article find links to article

signal is impressed into the magnetic field x,y area by varying the sine and cosine inputs at a precise time. It is widely used for wireless LANs , RFID

Function of a real variable (3,560 words) [view diff] exact match in snippet view article find links to article

polynomial functions, including constant functions and linear functions Sine and cosine functions Exponential function Some functions are defined everywhere

Bounded type (mathematics) (1,666 words) [view diff] exact match in snippet view article

with Q ( z ) = exp ⁡ ( | a | i z ) {\displaystyle Q(z)=\exp(|a|iz)} . Sine and cosine are of bounded type in the UHP. Indeed, sin ⁡ ( z ) = P ( z ) / Q (

Cis (mathematics) (2,340 words) [view diff] exact match in snippet view article

platform the fused operation is about twice as fast as calling the sine and cosine functions individually. d d z cis ⁡ z = i cis ⁡ z = i e i z {\displaystyle

Weierstrass elliptic function (4,401 words) [view diff] exact match in snippet view article find links to article

\quad t\mapsto (\sin t,\cos t).} Because of the periodicity of the sine and cosine R / 2 π Z {\displaystyle \mathbb {R} /2\pi \mathbb {Z} } is chosen

Binomial theorem (6,250 words) [view diff] exact match in snippet view article find links to article

with de Moivre's formula to yield multiple-angle formulas for the sine and cosine. According to De Moivre's formula, cos ⁡ ( n x ) + i sin ⁡ ( n x )

Taylor series (8,253 words) [view diff] exact match in snippet view article find links to article

polynomials, exponential function ex, and the trigonometric functions sine and cosine, are examples of entire functions. Examples of functions that are not

Square root of 2 (5,701 words) [view diff] exact match in snippet view article find links to article

= ⁠1/√2⁠, along with the infinite product representations for the sine and cosine, leads to products such as 1 2 = ∏ k = 0 ∞ ( 1 − 1 ( 4 k + 2 ) 2 )

Indian people (7,621 words) [view diff] exact match in snippet view article find links to article

equations. Chakravala method, sign convention, madhava series, and the sine and cosine in trigonometric functions can be traced to the jyā and koti-jyā. Notable

Pi (17,481 words) [view diff] exact match in snippet view article find links to article

trigonometric functions have periods that are multiples of π; for example, sine and cosine have period 2π, so for any angle θ and any integer k, sin ⁡ θ = sin

Lists of integrals (5,611 words) [view diff] exact match in snippet view article find links to article

step function. If we also use the fact that the absolute values of sine and cosine are periodic with period π, then we get: ∫ | sin ⁡ a x | d x = 2 a

Synchronous coefficient of drag alteration (2,152 words) [view diff] exact match in snippet view article find links to article

using trigonometric identities results in a sum of constant terms, sine and cosine, at angular frequency 2 ω {\displaystyle 2\omega } . The next calculations

Integration by reduction formulae (2,235 words) [view diff] exact match in snippet view article find links to article

following integrals contain: Factors of sine Factors of cosine Factors of sine and cosine products and quotients Products/quotients of exponential factors and

Bioche's rules (1,160 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \sin t,\tan t,\cos(2t),\tan(t/2)} ), in the case of hyperbolic sine and cosine, a good change of variable is u = cosh ⁡ ( t ) {\displaystyle u=\cosh(t)}

Lode coordinates (1,685 words) [view diff] exact match in snippet view article find links to article

\theta _{s}} can be shown by applying a trigonometric identity relating sine and cosine by a shift cos ⁡ ( 3 θ c ) = sin ⁡ ( 3 θ s ) {\displaystyle \cos(3\theta

Integration by parts (6,875 words) [view diff] exact match in snippet view article find links to article

{\displaystyle v^{(n)}} are readily available (e.g., plain exponentials or sine and cosine, as in Laplace or Fourier transforms), and when the nth derivative

L'Hôpital's rule (7,121 words) [view diff] exact match in snippet view article find links to article

many common functions have continuous derivatives (e.g. polynomials, sine and cosine, exponential functions), so this special case covers most applications

Screw theory (4,395 words) [view diff] exact match in snippet view article find links to article

ẑ = (φ, d) define a dual angle, then the infinite series definitions of sine and cosine yield the relations sin ⁡ z ^ = ( sin ⁡ φ , d cos ⁡ φ ) , cos ⁡ z ^

Pauli matrices (7,437 words) [view diff] exact match in snippet view article find links to article

{\sigma }}\,.} Matrix exponentiating, and using the Taylor series for sine and cosine, e i a ( n ^ ⋅ σ → ) = ∑ k = 0 ∞ i k [ a ( n ^ ⋅ σ → ) ] k k ! = ∑

Polar coordinate system (6,687 words) [view diff] exact match in snippet view article find links to article

Cartesian coordinates x and y by using the trigonometric functions sine and cosine: x = r cos ⁡ φ , y = r sin ⁡ φ . {\displaystyle {\begin{aligned}x&=r\cos

Casus irreducibilis (3,373 words) [view diff] exact match in snippet view article find links to article

roots and trisectability can also be extended to some cases where the sine and cosine of the given angle is irrational. Consider as an example the case where

Gupta Empire (8,556 words) [view diff] exact match in snippet view article find links to article

Varāhamihira wrote the Pancha Siddhanta developing various formulas relating sine and cosine functions. Yativṛṣabha made contributions on units of measurement.

Mathematics (15,696 words) [view diff] exact match in snippet view article find links to article

Indian mathematics include the modern definition and approximation of sine and cosine, and an early form of infinite series. During the Golden Age of Islam

Proof that π is irrational (5,785 words) [view diff] exact match in snippet view article find links to article

have F ″ + F = f . {\displaystyle F''+F=f.} The derivatives of the sine and cosine function are given by sin' = cos and cos' = −sin. Hence the product

Wave (7,836 words) [view diff] exact match in snippet view article find links to article

combination of two sine waves with phases of zero and a quarter cycle, the sine and cosine components, respectively. A plane wave is a kind of wave whose value

Function (mathematics) (11,317 words) [view diff] exact match in snippet view article

Graph of two trigonometric functions: sine and cosine.

Hankel transform (4,204 words) [view diff] exact match in snippet view article find links to article

1145/317275.317284. Knockaert, Luc (2000). "Fast Hankel transform by fast sine and cosine transforms: the Mellin connection". IEEE Trans. Signal Process. 48

Formative assessment (7,558 words) [view diff] exact match in snippet view article find links to article

looking to each other to gain knowledge. "You seem to be confusing sine and cosine. Talk to Katie about the differences with the two." "Compare your work

List of incomplete or incorrect mathematical proofs (4,299 words) [view diff] exact match in snippet view article find links to article

definition of pointwise convergence. For example, a Fourier series of sine and cosine functions, all continuous, may converge pointwise to a discontinuous

Associated Legendre polynomials (5,475 words) [view diff] exact match in snippet view article find links to article

there are 2ℓ + 1 functions for the various values of m and choices of sine and cosine. They are all orthogonal in both ℓ and m when integrated over the surface

Series (mathematics) (9,694 words) [view diff] exact match in snippet view article

expansion of sines and cosines, of multiple arcs in powers of the sine and cosine of the arc had been treated by Jacob Bernoulli (1702) and his brother

List of Egyptian inventions and discoveries (17,995 words) [view diff] exact match in snippet view article find links to article

formulas for sine and cosine that are today known as Ptolemy's formulas, although Ptolemy himself used chords instead of sine and cosine. Ptolemy further

Oort constants (4,693 words) [view diff] exact match in snippet view article find links to article

}_{R_{0}}d\cdot \cos ^{2}\left(l\right)-\Omega d\\\end{aligned}}} Using the sine and cosine half angle formulae, these velocities may be rewritten as: V obs, r

Normal distribution (22,467 words) [view diff] exact match in snippet view article find links to article

of the Box–Muller method which does not require computation of the sine and cosine functions. In this method, U and V are drawn from the uniform (−1,1)

Timeline of scientific discoveries (10,369 words) [view diff] exact match in snippet view article find links to article

to 5th centuries: The modern fundamental trigonometric functions, sine and cosine, are described in the Siddhantas of India. This formulation of trigonometry

Spinodal decomposition (6,641 words) [view diff] exact match in snippet view article find links to article

mathematically represented by sines and cosines. Due to the properties of sine and cosine, it is possible to recover the amount of each wave in the sum by an

Spherical harmonics (12,420 words) [view diff] exact match in snippet view article find links to article

\theta )\ \cos(m\varphi )&{\text{if }}m>0\,.\end{cases}}} The same sine and cosine factors can be also seen in the following subsection that deals with

Hyperbola (13,551 words) [view diff] exact match in snippet view article find links to article

{\displaystyle y=1/x} is a rectangular hyperbola. Using the hyperbolic sine and cosine functions cosh , sinh {\displaystyle \cosh ,\sinh } , a parametric

List of British innovations and discoveries (13,433 words) [view diff] exact match in snippet view article find links to article

multiplication as well as the abbreviations "sin" and "cos" for the sine and cosine functions – William Oughtred Discovery of the "White Spot" on Saturn

History of Grandi's series (6,535 words) [view diff] case mismatch in snippet view article find links to article

authors list (link) Earnshaw, Samuel (1844-12-09). "On the Values of the Sine and Cosine of an Infinite Angle". Transactions of the Cambridge Philosophical

Edward Sang (5,913 words) [view diff] exact match in snippet view article find links to article

349–352 link Edward Sang, On a new investigation of the series for the sine and cosine of an arc, Proceedings of the Royal Society of Edinburgh, volume 9

Rule of marteloio (8,275 words) [view diff] exact match in snippet view article find links to article

although trigonometry was only in its infancy in Christian Europe, sine and cosine tables were already known in Arab mathematics. The Kingdom of Majorca

Singular spectrum analysis (6,725 words) [view diff] exact match in snippet view article find links to article

Fourier Analysis In contrast with Fourier analysis with fixed basis of sine and cosine functions, SSA uses an adaptive basis generated by the time series

List of English inventions and discoveries (16,728 words) [view diff] exact match in snippet view article find links to article

symbol for multiplication and the abbreviations "sin" and "cos" for the sine and cosine functions devised by William Oughtred (1574–1660) in Clavis Mathematicae

History of mathematical notation (11,512 words) [view diff] exact match in snippet view article find links to article

his proportionality sign (∷) and abbreviations sin and cos for the sine and cosine functions. Albert Girard also used the abbreviations 'sin', 'cos' and

X86 instruction listings (12,793 words) [view diff] exact match in snippet view article find links to article

compliant floating-point partial remainder. FPREM1 D9 F5 Floating-point sine and cosine. Computes two values S = sin ⁡ ( k ∗ s t ( 0 ) ) {\displaystyle S=\sin

Marcum Q-function (7,425 words) [view diff] exact match in snippet view article find links to article

express the Bessel functions with half-integer as sum of hyperbolic sine and cosine functions: I n + 1 2 ( z ) = 2 z π [ g n ( z ) sinh ⁡ ( z ) + g − n

Basil Hiley (11,854 words) [view diff] exact match in snippet view article find links to article

operator equations are analogous to the two equations that involve the sine and cosine bracket, and that the quantum phase equation has apparently not been

Fokas method (5,052 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \lambda } -plane, wheres the analogous equations for the sine and cosine transforms are valid only for λ {\displaystyle \lambda } real. The

Product operator formalism (5,744 words) [view diff] exact match in snippet view article find links to article

the final equality follows from recognising the Taylor series for sine and cosine. Now suppose that the density operator at time zero is ρ ( 0 ) = A