# cosine

## Definitions

• WordNet 3.6
• n cosine ratio of the adjacent side to the hypotenuse of a right-angled triangle
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Webster's Revised Unabridged Dictionary
• n Cosine (Trig) The sine of the complement of an arc or angle. See Illust. of Functions.
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Century Dictionary and Cyclopedia
• n cosine In trigonom., the sine of the complement of a given angle (whose cosine it is). If from the vertex of the angle as a center a circle is described with any radius, the cosine is the ratio of the distance from the center to the foot of a perpendicular let fall from the point of intersection of one side with the circle upon the other to the radius; or, if the radius is taken as unity, the cosine is that distance itself. The cosine of the arc or angle is the sine of its complement, and vice versa. See complement. Abbreviated cos.
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## Etymology

Webster's Revised Unabridged Dictionary
For co,. sinus, an abbrev. of L. complementi sinus,

## Usage

### In literature:

Cosin Elloees is the prettiest one of all.
"Jewel" by Clara Louise Burnham
McTurk may have some conception of the meaning of it; but Beetle is as the brutes that perish about sines and cosines.
"Stalky & Co." by Rudyard Kipling
Goe, call I pray thee, our kinsfolke and cosins, that they maye helpe vs to morowe betimes.
"The Palace of Pleasure, Volume 1" by William Painter
Went with my Wife and dear cosin to St. Germains, and kissed the Queene-mother's hand.
"Sylva, Vol. 1 (of 2)" by John Evelyn
In order to make any solution at all possible you have assumed cosine squared theta negligible.
"Spacehounds of IPC" by Edward Elmer Smith
Mrs Cosin, the landlady of the White Hart, prepared a very good supper for the Commissioners.
"The King's Daughters" by Emily Sarah Holt
Mr. Cosin was the gentleman who had laid his whip across the saucy lout's back at the time the French prisoners were marching into the barracks.
"The French Prisoners of Norman Cross A Tale" by Arthur Brown
Why grutchen here his cosin and his wif Of his welfare, that loven him so wel?
"Blackwood's Edinburgh Magazine, Volume 57, No. 356, June, 1845" by Various
Basire mentions three "imperfect" works of Bishop Cosin's in manuscript: viz.
"Notes and Queries, Number 33, June 15, 1850" by Various
Cosin, Bishop (1594-1672), 444.
"A History of English Literature" by George Saintsbury
Cosin's History of Transubstantiation, note on, 551.
"Notes and Queries, Index of Volume 5, January-June, 1852" by Various
COSIN and others; and Select Psalms and Hymns.
"Australia, its history and present condition" by William Pridden
Cosin occupies an interesting and peculiar position among the churchmen of his time.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 4" by Various
His father stood over him in wonder while he filled a sheet of paper with sines, cosines, secants, and such things.
"Harper's Round Table, June 4, 1895" by Various
The angle is then found by referring to a table of cosines.
"Turning and Boring" by Franklin D. Jones
Cosin, good day and health.
"Beaumont & Fletcher's Works (8 of 10)" by Francis Beaumont
And, seating himself beside Dirrik, he began to explain the mysteries of sine, cosine and tangent.
"Dry Fish and Wet" by Anthon Bernhard Elias Nilsen
The nine cosine-inclinations above are, as has been seen, connected by six equations.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
Cosin by John Parker, the Archbishop's eldest son, Jan. 5, 1593.
"Annals of the Bodleian Library, Oxford, A.D. 1598-A.D. 1867" by William Dunn Macray
Cosin (John), Bp., iii.
"The Works of Sir Thomas Browne" by Thomas Browne
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### In news:

In this paper, we argue that the agglomerative clustering with vector cosine similarity measure performs poorly due to two reasons.
Do Two Sines Equal A Cosine.
Dr Cosin Joins Doctors Of Central Connecticut.
Cosine Wherry, designed by John Hartsock, and launched it in Hancock Maine on May 24, 2012.
A relative newcomer, Cosine 's creativity and focus on data has propelled its success, writes Bill Britt.
Do Two Sines Equal A Cosine .
These figures show proofs of trigonometric addition and subtraction formulas for cosine and sine by Leonard M Smiley, University of Alaska Anchorage.
Early, boom-time hits Cerent, Siara, Extreme and CoSine brought the firm billions.
Cosine Wherry , designed by John Hartsock, and launched it in Hancock Maine on May 24, 2012.
Cosine Wherry, designed by John Hartsock, and launched it in Hancock Maine on May 24, 2012.
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### In science:

For each k-twisted sector, s and c are the vectors of sines and cosines respectively of the twist vector v, ǫ is the sign of the product of the components of the vector s.
Wess Zumino Couplings for Generalized Sigma Orbifold Fixed-points
Cycle lengths of the bit generator with Cosine weights (5).
Predicting and generating time series by neural networks: An investigation using statistical physics
The above result says that any stationary random process can be decomposed into a sum of sine and cosine functions with uncorrelated coeﬃcients.
Resampled random processes in gravitational-wave data analysis
Since the original sum was real, we can eliminate the roots of unity in this sum by taking the real part of ω−rs and writing everything in terms of cosines.
Random Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval
If we let z = ω r , where ω = e2π i/2m here rather than e2π i/4m as for the diagonals, we have ω−rs exp(x(ω r + ω−r )) = Xj∈Z As before, we now take 1/2m times the sum over all values of r to eliminate the terms for which j 6≡ s (mod 2m), and then take the real part of ω−rs to write everything in terms of cosines.
Random Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval
It can be shown easily that when a particle moves towards (+) direction ∆x > 0(µ > 0) in the boundary rest frame, the range of the pitch angle cosine in the ﬂuid frame is −ν < µ′ < 1, and for (-) direction ∆x < 0(µ < 0), the range becomes −1 < µ′ < −ν .
Application of random walk theory to the first order Fermi acceleration in shock waves
In order to apply the random walk theory described above to the shock acceleration, it is useful to consider the probability density of the pitch angle cosine µ′ when the particle which crossed the shock front with µ′ 0 returns to the front crossing the reverse direction.
Application of random walk theory to the first order Fermi acceleration in shock waves
The particle ﬁrst crosses the boundary toward (-) direction, i.e., from the downstream to the upstream with a pitch angle cosine µ′ 0 (< −ν ).
Application of random walk theory to the first order Fermi acceleration in shock waves
The probability density of the ﬁrst scattering point for the particle which crossed the boundary with pitch angle cosine µ′ 0 is determined by the scattering law (4).
Application of random walk theory to the first order Fermi acceleration in shock waves
For the downstream, the probability density of pitch angle cosine µ′ (< −ν ) at return for the particle which initially crossed the shock front with µ′ 0 (> −ν ) ((+) direction), PDW (µ′ ; µ′ 0 ), is calculated in a similar way.
Application of random walk theory to the first order Fermi acceleration in shock waves
The absorption probability of the particle injected in the upstream at the distance of a from the shock front and the pitch angle cosine µ′ , Pa (µ′ ), can be also calculated in a similar manner.
Application of random walk theory to the first order Fermi acceleration in shock waves
Our approximation (solid curves) gives a fairly good ﬁt to the Monte Carlo simulation (grey histograms) for all initial pitch angle cosine µ′ 0 .
Application of random walk theory to the first order Fermi acceleration in shock waves
Here, the initial pitch angle cosine µ0 is measured in the boundary rest frame.
Application of random walk theory to the first order Fermi acceleration in shock waves
Fig. 8 presents the total return probability PR (µ0 ) from the downstream for mildly high ν (ν = 1/3) as a function of initial pitch angle cosine µ0 , which is measured in the boundary rest frame.
Application of random walk theory to the first order Fermi acceleration in shock waves
Vf )2 dµ, where µ is the pitch angle cosine measured in the shock rest frame.
Application of random walk theory to the first order Fermi acceleration in shock waves
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