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|[[Sine]] |[[Hyperbolic sine]]

...en the two starting waves. To demonstrate the simplest case, between two [[sine wave]]s of equal [[amplitude]]: ...ession above (it can be said, the cosine factor is an ''envelope'' for the sine wave), whose frequency is (''f''₁+''f''₂)/2, that is,

...ngles]], the angle C, opposite the [[hypotenuse]] (c), is 90 degrees. The sine of 90 degrees is 1, so the equation reduces to:

...the reciprocal of the cosine, the '''cosecant''' is the reciprocal of the sine, and the '''cotangent''' is the reciprocal of the tangent.

multiplied by the [[sine]] of the angle between the sides.

*The [[sine]] of 1 radian is 0.841 470 985...

{{r|Sine}}

...umption for survival, survival manifested as [[reproductive success]], a ''sine qua non'' of evolution by means of [[natural selection]].

...tant in all branches of science and technology. It is possible to define sine and cosine in different ways. Two ways, one based on plane geometry and o ===Definition of sine and cosine in plane geometry===

...respect to the requirement that for a counterinsurgency to succeed, the ''sine qua non'' is to see the government as legitimate. This is especially compl

...nvelopes.png|right|150px|Top and bottom envelope functions for a modulated sine wave.}} ...ing its extremes in amplitude.<ref name=Johnson/> The figure illustrates a sine wave varying between an upper and a lower envelope. The envelope function m

Numerical Recipes in C. Fast Sine and Cosine transform. ...g the only antisimmetric modes can be performed with the [[DST]] (Discrete sine transform).

| '''Sine''' The earliest use of sine appears in the ''[[Sulba Sutras]]'' written in [[History of India|ancient I

...decompose it into its constituent frequencies. The main idea is to employ sine and cosine functions of a continuous range of frequencies (in fact from <ma

...rned. He famously declared that the vernacular with "without any rules" (''sine omnia regula''), by which of course he meant written, codified rules as tau

...mathematical objects. Examples of elementary functions include the [[sine|sine function]] and the [[logarithmic function]], which (denoting their argument ...plane]]. Given either of the non-right angles (which we call ''x''), the ''sine of x'' equals the ratio between the side opposite to the angle and the side

...or '''asign''', or '''arcsin''' is [[holomorphic function]], inverse of [[sine|sin]].

Numerical Recipes in C. Fast Sine and Cosine transform.

Cosine- and sine-type regular [[solid harmonics]] (normalized to unity) can be defined by th ...es, the cosine-type functions contain the factor cos |''m''| &phi; and the sine-type functions sin |''m''| &phi;. Hence the name. It is of some interest t

...the particle, the intensity ''B'' of the [[magnetic induction]], and the [[sine]] of the angle between the [[vector]]s '''v''' and '''B'''. The ''direction

...f the [[harmonic oscillator (classical)|harmonic oscillator]]s is given by sine-type functions, so that the time derivatives of the ''Q''_''t'''s ...ential equations are easily solved yielding the ''Q''_''t'''s as sine-type functions of time, see the article on [[harmonic oscillator (classical

...integral]]s of entire functions, for example the [[error function]] erf, [[sine integral]] Si and the [[Bessel function]] ''J''₀ are also entire

* Epistole sine nomine

...ellium, sed magnitudine paulo antecedunt mutilaeque sunt cornibus et crura sine nodis articulisque habent neque quietis causa procumbunt neque, si quo adfl

...and winning elections. Although a competitive party system is considered a sine qua non of modern [[democracy]], parties operate in many [[authoritarianism

The exponential is related to the [[trigonometric function]]s [[sine]] and [[cosine]] by ''[[de Moivre]]'s formula'':

...sical phenomena that are essential to his study. Reduction is a ''conditio sine qua non'' in the explanation of observations and is essential for the pro

...e obtained [[associated Legendre functions]] for ''m'' = 1 (linear in the sine of latitude angle). Legendre submitted his results to the [[Académie des

...ion excludes the function sin&omega;t, because the first derivative of the sine is the cosine which is not zero at ''t'' = 0. Hence the time function is of and that the sine function is odd, sin(&minus;''u'') = &minus;sin(''u'').

Numerical Recipes in C. Fast Sine and Cosine transform.

...ng|thumb|250px|Outcome of Newton's method applied to finding a root of the sine function. Initial values near 0 (blue) lead to 0 while initial values near .... If we start with <math>x_0</math> close to <math>\pi/2</math>, where the sine curve is horizontal, <math>x_1</math> may end up close to <math>n \pi</math

...that there is increasing resistance to the idea of "loyal opposition", a ''sine qua non'' of democracy. I am alarmed by the idea of an ostensible mediator

and so are [[sine]], [[cosine]] and the [[exponential function]].

...al of the Hohner piano through the filter, and modulated the filter with a sine-wave LFO. This made the filter rise and fall rapidly, creating a shifting t

..., i.e., &alpha;(''t'') linear in time ''t'', it follows that the EMF has a sine dependence on time and an [[alternating current]] will be induced.

...to &minus;''x''. There are several functions known to have this property (sine, cosine, exponent with imaginary argument), we choose fairly arbitrarily th

In similar way, 0 is fixed point of [[sine]] function, because <math>\sin(0)=0</math>.

...directly across the straits from Messana, and was comprised of citizens ''sine suffragio'' (citizens without voting rights) from Capua. Soon after the Mam

...s, fan fiction, martyrdom and war. As scripture, the Hebrew Bible is the ''sine qua non'' of [[Judaism]] and sacred to [[Christianity|Christians]]. As [[li

...een the gamma function of positive and negative numbers. The division by a sine, which is periodically zero, again indicates the existence of the gamma fun ...lection formulas, using only a few multiplications or an evaluation of the sine in the reflection formula. Listings of [[polynomial]]s and [[rational funct

We used here the relations well-known from [[trigonometry]] for the sine and cosine of a sum angle.

...aying what they called a 'three-tone sinusoidal replica', or a complicated sine wave sound, they found that people were able to perceive speech, when in fa

...|Modulated wave.png|right|150px|A modulated wave resulting from adding two sine waves of nearly identical wavelength and frequency.}} which uses the trigonometric formula for the addition of two sine waves, and the approximation &Delta;&lambda;<<&lambda;:

...e is no particle! The other way to satisfy this equality is to have the [[sine]] term vanish, which will happen if

...ion's belief that the conflict in Korea could be part of a wider war, only sine of the increase would go to direct support of the conflict in Korea. ...ion's belief that the conflict in Korea could be part of a wider war, only sine of the increase would go to direct support of the conflict in Korea.

...full and unconditional support of the Palestinian people is a condition [[sine qua non]] for activists to adopt, and we recognise that their attachment to

...s task is called ''complete''. Such basis sets are a generalization of the sine and cosine functions used in [[Fourier series]] to a wider set of functions

The sine and cosine functions are not [[one-to-one function|one-to-one]] and hence n

...the fixed point ''z'' as a function of time ''t'', we see the same type ([[sine]]-type) function as in figure 1. The number of times per second that the ve

...common form of transposon in [[human]]s is the [[Alu sequence]], a form of SINE. The [[Alu sequence]] is approximately 300 bases long and about 1000 copies