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...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

...ultimately, a continuous-wave transmitter &mdash; one that produced a pure sine-wave signal on a single frequency &mdash; would be far more efficient, part

...opagate posteriorly, giving the overall shape of a posteriorly propagating sine wave. In addition, all snakes are capable of [[concertina movement]]. This

...hich the denominator is unity. With this formula for the derivative of the sine, the radius of curvature becomes:

The following expression defines real spherical harmonics of cosine and sine type respectively:

...al to the object's speed, to the frame's rate of rotation, and also to the sine of the angle between the object's direction of movement and the frame's axi

...of the experiments on the auditory system have been performed with simple sine wave stimuli. Other experiments which have claimed to investigate the effec

...s. His nearest pronouncement seems to be ''Numquam ponenda est pluralitas sine necessitate'', which occurs in his theological work on the ''Sentences'' of

...power units that produce a [[square wave]] pattern instead of the normal [[sine wave]], making rapid zero crossings possible and minimizing the effects of

...anistan]], where development of a respected police force is considered a ''sine qua non'' for successful counterinsurgency.

==The fundamental units and processes of living things: the '''''sine qua non'''''==

In other words, '''''sine qua non''''' of the activity of living.