triangle

/ˈtɹaɪəŋɡəl/

/ˈtɹaɪˌæŋɡəl/

/ˈtɹaɪˌæŋɡəl/

PIE word
 *tréyes
From Middle English triangle, from Old French triangle, from Latin triangulum, noun use of adjective triangulus (“three-cornered, having three angles”), from trēs (“three”) + angulus (“corner, angle”), equivalent to tri- + angle.

The wedge-shaped character was the triangle, the archaic Paleolithic sign of the vulva; the pubic triangle was at the end of the phallic stylus.

1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 22:

(geometry) A polygon with three sides and three angles.


scalene

Borrowed from Late Latin scalēnus (“of unequal sides”), from Ancient Greek σκᾰληνός (skalēnós, “uneven, unequal”).

bor

scalene triangle

(trigonometry) Having sides all unequal in length.


scalene

scalene triangle
scalene triangle#English

(trigonometry) Ellipsis of scalene triangle..


polygonometry

en-noun

polygonometry (usually uncountable, plural polygonometries)


trigonometry

trigonometry (countable and uncountable, plural trigonometries)

/ˌtɹɪɡəˈnɒmətɹi/

PIE word
 *tréyes
From 1610s, from New Latin trigōnometria, from Ancient Greek τρίγωνον (trígōnon, “triangle”) + μέτρον (métron, “measure”), equivalent to trigono- + -metry.

EtymOnLine

Douglas Harper (2001–2024) “trigonometry”, in Online Etymology Dictionary.

Trigonometry emerged in the Hellenistic world during the 3rd century BCE from applications of geometry to astronomy; the Greeks focused on the calculation of chords, while mathematicians in India created the earliest known tables of values for trigonometric functions such as sine.

Historically, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics and navigation.

Trigonometry was originally the science which treated only of the sides and angles of plane and spherical triangles; but it has been recently extended so as to include the analytic treatment of all theorems involving the consideration of angular magnitudes.

1892, Edward Albert Bowser, A Treatise on Plane and Spherical Trigonometry, D. C. Heath & Co., page 1:

In fact, the earliest practical uses of trigonometry were in the fields of astronomy and hence navigation.

2013, Paul Abbott, Hugh Neill, Trigonometry: A Complete Introduction, Hachette, unnumbered page:

The properties of these new trigonometries and identities flowing from the definitions are then developed.
The trigonometries derived from these generalizations will be jointly termed "The Fractional Trigonometry."

2016, Carl F. Lorenzo, Tom T. Hartley, The Fractional Trigonometry, Wiley, page 8:

mathematical analysis
mathematical analysis

right-angled triangle
right-angled triangle

trigonometric function
trigonometric function

(geometry, mathematical analysis) The branch of mathematics that deals with the relationships between the sides and angles of (in particular) right-angled triangles, as represented by the trigonometric functions, and with calculations based on said relationships.


cosine

From co- + sine, short for complementi sinus in Latin, meaning “sine of the complement”. Doublet of cosinus.

(trigonometry) In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse. Symbol: cos


tangent

Borrowed from Latin tangentem, the accusative of tangēns (“touching”) (in the phrase līnea tangēns (“a touching line”)), the present participle of the verb tangō (“touch”, verb), from Proto-Italic *tangō, from Proto-Indo-European *teh₂g- (“to touch”).
Cognate with Old English þaccian (“to touch lightly, pat, stroke”). More at thack, thwack.

cog

(mathematics) A function of an angle that gives the ratio of the sine to the cosine, in either the real or complex numbers. Symbols: tan, tg.


tangent

The collision occurred on a two-mile stretch of tangent track.

(rail transport, of track) Straight; not horizontally curved.


sine

Borrowed from Latin sinus (“curve, bend; bosom”), a translation of Arabic جَيْب (jayb, “bosom”), a misidentification of the notation جيب (j-y-b), written without vowel diacritics, standing for Arabic جِيبَ (jība, “sine”), in turn from Sanskrit ज्या (jyā, “sine, chord, bowstring”) through the similar Sanskrit जीव (jīva, “sine, chord, life, existence”). Doublet of sinus.

der

(trigonometry, mathematics) In a right triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse.


gradian

LL-Q1860 (eng)-Flame, not lame-gradian.wav

(geometry, trigonometry) A unit of angle equal to 0.9 degree, so that there are 100 gradians in a right angle.


secant

LL-Q1860 (eng)-Flame, not lame-secant.wav

From Latin secāns, present participle of secō (“to cut”).

(trigonometry) In a right triangle, the reciprocal of the cosine of an angle. Symbol: sec


sine wave

(trigonometry, signal processing) A periodically oscillating waveform as described by the sine function, possibly multiplied by some amplitude, shifted by some phase, and translated by an additive constant.


arccosine

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the cosine function.


arcsine

/ˈɑːɹkˌsaɪn/

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the sine function. Symbol: arcsin, sin⁻¹


hypotenuse

From Latin hypotenusa, from Ancient Greek ὑποτείνουσα πλευρά (hupoteínousa pleurá, “side subtending [the right angle]”), from ὑποτείνουσα (hupoteínousa, “stretching, extending, subtending”), active participle of ὑποτείνω (hupoteínō, “subtend, stretch under”).

uder

ὑποτείνουσα πλευρά

Coordinate term: cathetus

(geometry) The side of a right triangle opposite the right angle.

وَتَر

the side of a right triangle opposite the right angle


arc-

From Latin arcus (“bow, arc”), as they represent an angle or arc. Compare etymology of arch.

arc-sine (British), arcsine (US)

arctan

inverse trigonometric function
inverse trigonometric function#English

(mathematics) Used to form the names of inverse trigonometric functions, and the symbols for these functions.


simple harmonic motion

en-noun

simple harmonic motion (plural simple harmonic motions)

(mathematics, mechanics) oscillating motion (as of a pendulum) in which the acceleration of the oscillator has an equal magnitude but opposite direction to the displacement of it from the equilibrium position.


orthogon

LL-Q1860 (eng)-Flame, not lame-orthogon.wav

(trigonometry) A multi-dimensional figure in which all sides result in a right-angle, typically surpassing the restrictions of 3 dimensions.


waveform

LL-Q1860 (eng)-Flame, not lame-waveform.wav

independent variable
independent variable

(mathematics) The shape of a wave function represented by a graph showing some dependent variable as function of an independent variable.


trigonometric function

trigonometric function (plural trigonometric functions)

(trigonometry) Any function of an angle expressible as the ratio of two of the sides of a right triangle that has that angle (e.g., sine), or that subtracts 1 from such a ratio or subtracts such a ratio from 1 (e.g., coversed sine).


cosecant

LL-Q1860 (eng)-Flame, not lame-cosecant.wav

(trigonometry) In a right triangle, the reciprocal of the sine of an angle. Symbols: cosec, csc


cotangent

LL-Q1860 (eng)-Flame, not lame-cotangent.wav

(trigonometry) In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg, or ctn


arctangent

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the tangent function. Symbol: arctan, tan⁻¹


acute-angled

(trigonometry) Of a triangle: having three acute angles.


sinus

Learned borrowing from Latin sinus (“a bent surface, curve, hollow”). Doublet of sine.

lbor

(anatomy, zootomy) A pouch or cavity in a bone or other tissue, especially one in the bones of the face or skull connecting with the nasal cavities (the paranasal sinus).

sinus

So, in the helicopteron, as the helix is at the same time a sustaining plane, it should be likened to a surface moving horizontally, and in which, consequenty, the resistance to motion will be to the lifting power as the sinus is to the cosinus of the angle formed by such plane with the horizon.

1884 November 29, “Aerial Navigation”, in Scientific American: A Weekly Journal of Practical Information, Art, Science, Mechanics, Chemistry, and Manufactures, volume LI, number 22, New York, N.Y.: Munn & Co., translation of original by Victor Tatin in La Nature, page 342, column 1:

The variations are described in terms of cycles of sinuses and cosinuses.

1996, Pentti Zetterberg, Matti Eronen, Markus Lindholm, “Construction of a 7500-Year Tree-Ring Record for Scots Pine (Pinus sylvestris, L.) in Northern Fennoscandia and its Application to Growth Variation and Palaeoclimatic Studies”, in Heinrich Spiecker, Kari Mielikäinen, Michael Köhl, Jens Peter Skovsgaard, editors, Growth Trends in European Forests (European Forest Institute Research Report; No. 5), Springer-Verlag Berlin Heidelberg, →ISBN, page 15:

Basically, the rotation of the matrix of the factor loadings L represents its post-multiplication, i.e. L* = LO by the rotation matrix O, which itself resembles one of the matrices included in the classical rotational Lie groups SO(m) (containing the specific m–fold combination of sinuses and cosinuses.

2007, Vladimir G. Ivancevic, Tijana T. Ivancevic, “Introduction: Human and Computational Mind”, in Computational Mind: A Complex Dynamics Perspective (Studies in Computational Intelligence; 60), Springer-Verlag Berlin Heidelberg, →ISBN, →LCCN, section 1 (Natural Intelligence and Human Mind), pages 60–61:


trig

en-noun

trig (countable and uncountable, plural trigs)


gon

From Ancient Greek γωνία (gōnía, “angle”).

(geometry, trigonometry) One hundredth of a right angle; a gradian.


arccos

arccos (1/2ϕ)=2π/5

[…]with the appropriate constraint angles measured in terms of the arccoses and arctans.

1973, The Soviet Economy in Regional Perspective, Praeger Publishers, page 3:


arctan

tan (arctan 2/2)=1/ϕ


arcsinh

/ˈɑː(ɹ)kˌʃaɪn/

(trigonometry) Alternative form of arsinh (“the inverse hyperbolic sine function”)


arctanh

/ˈɑː(ɹ)kˌtænʃ/

(trigonometry) Alternative form of artanh (“the inverse hyberbolic tangent function”)


arcsech

/ˈɑː(ɹ)kˌsɛt͡ʃ/

(trigonometry) Alternative form of arsech (“the inverse hyberbolic secant function”)


arcsch

/ˈɑː(ɹ)ˌkəʊsɛt͡ʃ/

(trigonometry) The area hyperbolic cosecant function, i.e., the inverse hyperbolic cosecant function.


haversin

(trigonometry) Abbreviation of haversine.


hacoversin

(trigonometry) Abbreviation of hacoversed sine.


hacoversed sine

hacoversed sine (plural hacoversed sines)

(trigonometry) The trigonometric function equal to half the coversed sine. Abbreviation: hacoversin


versine

The simplest method of calculating the radius of a curve in situ is to measure the versine; in railway practice this is done by extending a tape 66 ft. (1 ch.) long in a straight line or chord between two points on the periphery of a curve, and then measuring the maximum distance of the rail from the chord at the centre of the 66 ft. The radius in chains is found by dividing the versine in inches into 99. Thus if a versine measures 3 in., the radius will be 33 ch.

1941 September, “The Why and the Wherefore: Curves”, in Railway Magazine, page 430:


coversed sine

From contraction of complement + versed sine.

The cosine of an arc is the sine of its complement.† In like manner, the coversed sine, cotangent, and cosecant of an arc, are respectively the versed sine, tangent, and secant of its complement.

1825, Jas Thomson, Elements of Plane and Spherical Trigonometry, page 2:

At the top of the page on the left-hand side is placed the number of degrees, and in the left-hand column each minute of the degree, opposite to which are arranged the numerical values of the sine, coversed sine, &c, of the corresponding angle in those columns, at the top of which those terms are placed.

1830, W. Hopkins, “Book II: Elements of Trigonometry”, in Geometry, Plane, Solid, and Spherical, page 46:

For the coversed sine; subtract the sine of the angle from 1. Thus, for the same angle we have the coversed sine,
1 — ·36650 = ·6335.

1838, William Grier, The Mechanic′s Pocket Dictionary, page 21:

Hence the cosines and versed sines of zenith distances are respectively equal to the sines and coversed sines of the corresponding angular elevations.

1871, Homersham Cox, The Law and Science of Ancient Lights, 2nd edition, page 109:

(trigonometry) The trigonometric function 1 − sin(x).


haversed sine

(trigonometry, rare) The trigonometric function defined as half the versed sine. Abbreviation: haversin


versed sine

From New Latin sinus versus (“flipped sine”); the sine function being sometimes called sinus rectus.

For the divisions, to be laid on this line, are the differences between the logarithm versed sine of 180°, and the logarithm versed sines of the successive arcs.

1753, John Robertson, “The Construction of the Logarithmic Lines on the Gunter′s Scale”, in Philosophical Transactions: 1750-1755, Great Britain: Royal Society, page 340:

But if the given arch exceed 90°, find the natural co-sine of its supplement, which add to 1000000, and the sum will be the natural versed sine required.

1805, John William Norie, A New and Complete Epitome of Practical Navigation, page xxii:

The Natural Sines in this table are fractions (radius being unit); and are particularly adapted to Dunthorne′s and other methods of clearing the moon′s distance from the effects of parallax and refraction, where natural sines or versed sines are used ;[…].

1806, John Garnett, Tables Requisite To Be Used with The Nautical Ephemeris, page 41:

(trigonometry) The trigonometric function 1 − cos(x).


unit circle

(trigonometry, the unit circle) The circle of radius 1 with centre at the origin, used in defining trigonometric functions.

jednotková kružnice

circle of radius 1 with centre at the origin, used in trigonometry


havercosine

(trigonometry) the trigonometric function (1 + cos(x)) / 2, equal to half the vercosine


exsec

(trigonometry) Abbreviation of exsecant.


excsc

(trigonometry) Abbreviation of excosecant.


excosecant

(trigonometry) The trigonometric function csc(x) − 1. Abbreviation: excsc


exsecant

(trigonometry) The trigonometric function sec(x) − 1. Abbreviation: exsec


Pythagorean theorem

Named after Pythagoras (from Ancient Greek Πυθαγόρας (Puthagóras)), the Greek mathematician and philosopher who by tradition is credited with the theorem’s discovery and proof.

The Pythagorean theorem only applies to right triangles.

(geometry) A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides.


trigonometric

/ˌtɹɪɡ ə nəˈmɛ tɹɪk/

(mathematics) of, relating to, or constructed using trigonometry


circular function

circular function (plural circular functions)

trigonometric function
trigonometric function#English

(trigonometry) Synonym of trigonometric function


cofunction

Cosine and sine are each other's cofunctions.

(mathematics) The trigonometric function of the complement of the supplied angle.

(programming) A costatement that takes the form of a function and can accept parameters and return a value.


inverse trigonometric function

inverse trigonometric function (plural inverse trigonometric functions)

inverse trigonometric functions (plural)

(mathematics) A function that is the inverse of an appropriate restriction of a trigonometric function.


trigonometric cofunction

trigonometric cofunction (plural trigonometric cofunctions)

(mathematics) Either of a pair of trigonometric functions that have equal values when their arguments are complementary angles, e.g. sine and cosine.


In the public sector, we have not really created 360-degree accountability. It is more like 360-degree harassment.

2001, Robert D. Behn, Rethinking Democratic Accountability, Brookings Institution Press, →ISBN, page 199:

Implement a 360-degree system regularly.

2002, Manuel London, Leadership Development: Paths to Self-insight and Professional Growth, Lawrence Erlbaum Associates, →ISBN, page 155:

The overall grade is a compilation of input from these sources. Thus it provides a true 360-degree view of the officer evaluated.

2006, Thomas X. Hammes, The Sling and the Stone: On War in the 21st Century, Zenith Imprint, →ISBN, page 238:

(by extension) Comprehensive; incorporating all points of view.


cosinus

Learned borrowing from New Latin cosinus, abbreviation of complementi sinus. Doublet of cosine.

lbor

When I came to these very buildings to pass my examination I knew far better the names of all the plants in this garden than the theory of the cubic roots or the long formulæ of the sum of two cosinus.

1884, A[lbert] A[ugustin] Fauvel, Chinese Plants in Normandy, Hong Kong: […], page 4, column 1:

So, in the helicopteron, as the helix is at the same time a sustaining plane, it should be likened to a surface moving horizontally, and in which, consequenty, the resistance to motion will be to the lifting power as the sinus is to the cosinus of the angle formed by such plane with the horizon.

And according to our choice of a symmetrical conjunction or opposition, all the cosinuses are reduced to 1, namely to coefficients build up solely by scalar Keplerian elements a, e.

1949, Contributions from the Astronomical Institute of the Charles University Prague, page 38:

The variations are described in terms of cycles of sinuses and cosinuses.

Basically, the rotation of the matrix of the factor loadings L represents its post-multiplication, i.e. L* = LO by the rotation matrix O, which itself resembles one of the matrices included in the classical rotational Lie groups SO(m) (containing the specific m–fold combination of sinuses and cosinuses.


sinusoid

From the French sinusoïde, equivalent to sinus + -oid.

Temperature during the week can be represented with a sinusoid.

(mathematics) A curve having the shape of a sine wave.


sinusoid

en-adj

sinusoid (comparative more sinusoid, superlative most sinusoid)

more sinusoid (comparative)
most sinusoid (superlative)


Fourier series

Named after French mathematician and physicist Joseph Fourier (1768-1830), who pioneered research into such series and their application to problems of heat transfer and vibration.

1951 [Blackie & Son], R. C. H. Young (translator), Konrad Knopp, Theory and Application of Infinite Series, [1947, Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, 4th Edition], 1990, Dover, Unabridged unaltered reprint of 2nd English Edition, page 493,
As we have seen (pp. 369—370), the question of the necessary and sufficient conditions under which the Fourier series of an integrable function converges and represents the given function is one which presents very great difficulties.

2001, David Cruz-Uribe (translator), Javier Duoandikoetxea Zuazo, Fourier Analysis, [1995, Javier Duoandikoetxea Zuazo, Análisis de Fourier], American Mathematical Society, page 20,
There are excellent discussions of Fourier series and integrals in Katznelson [10] and Dym and McKean [4]. The book by R. E. Edwards [5] is an exhaustive study of Fourier series from a more modern perspective.

Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable.

2006, K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3rd edition, Cambridge University Press, page 415:

(mathematics, mathematical analysis) Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials).

フーリエ級数

フーリエきゅうすう,fūrie kyūsū


arccotangent

(trigonometry) An inverse of the cotangent function. Symbol: arccot


sine ratio

(trigonometry) The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.


arccosecant

(trigonometry) function that is the compositional inverse of the cosecant function. Symbol: arccsc


arcsecant

(trigonometry) function that is the compositional inverse of the secant function. Symbol: arcsec


nine-point circle

en-noun

nine-point circle (plural nine-point circles)

So called because the circle passes through nine points of interest: the feet of the three altitudes, the centers of the three sides, and the midpoints of the segments which join the triangle's vertices with its orthocenter.

That circle which passes through the feet of the altitudes of a given triangle.


ar-

Shortened from area (because the function describes the area under a hyperbola), by analogy with arc-, the corresponding prefix for the circular trigonometric functions.

inverse hyperbolic function
inverse hyperbolic function#English

(trigonometry) Used to form the names of inverse hyperbolic functions, and the symbols for these functions.


square wave

(calculus, engineering, signal processing) A function or waveform that alternates regularly and instantaneously between two levels.


law of cosines

(trigonometry) A generalization of the Pythagorean theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.


gyrotrigonometry

(hyperbolic geometry) The use of gyroconcepts to study hyperbolic triangles.


gyrotriangle

(hyperbolic geometry) A triangle in gyrovector space.


Fourier sine series

Fourier sine series (plural Fourier sine series)

a Fourier series consisting solely of sine functions


Fourier cosine series

Fourier cosine series (plural Fourier cosine series)

a Fourier series consisting solely of cosine functions


law of sines

(trigonometry) A statement that relates the lengths of the sides of a triangle to the sines of its angles.


SOHCAHTOA

LL-Q1860 (eng)-Flame, not lame-SOHCAHTOA.wav

(mnemonic, trigonometry) sine: opposite over hypotenuse, cosine: adjacent over hypotenuse, tangent: opposite over adjacent


Pythagorean trigonometric identity

Pythagorean trigonometric identity (plural Pythagorean trigonometric identities)

Pythagorean trigonometric identities (plural)

(trigonometry) The equality sin (x)²+ cos (x)²=1, holding for all real and complex x, equivalent to the application of the Pythagorean theorem to the unit circle.

jedynka trygonometryczna

statement that sum of squares of sine and cosine equals one


suversed

The key insight was to replace the law of cosines by a law of versed sines or a law of suversed sines, where the suversed sine of an angle is the versed sine of the supplement of that angle.

2015, Maria Zack, Elaine Landry, Research in History and Philosophy of Mathematics, page 45:

(trigonometry) versed and belonging to the supplement


law of tangents

(trigonometry) A statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.


trigonometrical station

trigonometrical station (plural trigonometrical stations)

triangulation pillar
triangulation pillar#English


TOA-CAH-SOH

Inversion of SOH-CAH-TOA, nearly homophonic with Hokkien 大跤嫂 (tōa-kha-só, literally “middle-aged woman with huge feet”).

der

(Singapore, mnemonic, trigonometry, humorous) Synonym of SOHCAHTOA


subtendent

LL-Q1860 (eng)-Flame, not lame-subtendent.wav

Lastly, if you put BC the lesser of the sides, including the right angle for Radius, the greater side, AC, including the right angle is the tangent of ABC, the greater acute angle opposite; and the subtendent A B, is the secant of the same acute angle.

1642, Bartholomäus Pitiscus, Trigonometry: Or, The Doctrine of Triangles., page 91:

The very Subtendent line is found of an odde part; but the very subtendent of an even part is not found at one operation, but onely the Square of the Subtendent; and the greater the number of parts be, so much harder it willbe to finde out the subtendent.

1657, Johannes Jonstonus, An History of the Constancy of Nature:

The first figure, Vale, hath but one mood, and therefore of as great extent as it selfe, which is Upalem; whose nature is to let us know, whan a plane right angled triangle is given us to resolve, whose subtendent and one of the obliques is proposed, and one of the ambients required, that we must have recourse unto its resolver, which being Rad_U_Sapy→Yr sheweth, that if we joyne the artificiall sine of the angle opposite to the die demanded with the Logarithm of the subtendent, the summe searched in the canon of absolute numbers will afford us the Logarithm of the side required.

1834, Thomas Urquhart, Lord Thomas Maitland Dundrennan, The Works of Sir Thomas Urquhart of Cromarty, Knight, page 81:

For example, even if there were no possible quantity, mathematicians could say that if it was possible to make a right angled triangle, it was something assured that the hypotenuse or the subtendent of the right angle would make a square equal to the squares of the other two sides

1994, Alistair Cameron Crombie, Styles of Scientific Thinking in the European Tradition, page 840:

(geometry, trigonometry) The side that subtends (is opposite) a specified angle;


base angle

(trigonometry) Either of the two angles that intersect with the base of a triangle.


artanh

/ˈɑː(ɹ)ˌtænʃ/

(trigonometry) The area hyperbolic tangent function; i.e., the inverse hyperbolic tangent function (or hyperbolic arctangent)


arcosh

/ˈɑː(ɹ)ˌkɒʃ/

(trigonometry) The area hyperbolic cosine function, i.e., the inverse hyperbolic cosine function.


arcoth

/ˈɑː(ɹ)ˌkɒθ/

(trigonometry) The area hyperbolic cotangent function, i.e., the inverse hyperbolic cotangent function.


arsech

/ˈɑː(ɹ)ˌsɛt͡ʃ/

(trigonometry) The area hyperbolic secant function, i.e., the inverse hyperbolic secant function.


arsinh

/ˈɑː(ɹ)ˌsaɪnʃ/

/ˈɑː(ɹ)ˌʃaɪn/

(trigonometry) The area hyperbolic sine function, i.e., the inverse hyperbolic sine function.


scaline

scaline triangle


inverse tangent

en-noun

inverse tangent (plural inverse tangents)


scalenous

(trigonometry) Obsolete form of scalene.


goat grazing problem

goat grazing problem (plural goat grazing problems)

The problem: given a field of radius 1, and a goat tied to a point on the edge of said field; how long a rope should the goat be tied to, so that the goat has access to exactly half of the field? Equivalently: given a unit circle C and a point P on the rim of C, what is the value of r such that exactly half of the area within C, is within distance r of point P?

The same problem generalized to any number of dimensions: given a unit n-sphere (n-dimensional hypersphere) S, and a point P on the edge of S, what is r such that exactly one-half of the space (content) within S, is within distance r of P?


goat problem

goat grazing problem
goat grazing problem#English


trigonometric identity

trigonometric identity (plural trigonometric identities)

The trigonometric identity sin(2x) = 2sin(x)cos(x).

(mathematics, trigonometry) A trigonometric equation that is true for all values of the input variable for which both sides of the equation are defined.


versed cosine

(trigonometry) The trigonometric function 1 + cos(x).


head

From each word's initial letter forming SOHCAHTOA.

Another high school teacher told me that he uses a similar acrostic, but his is as follows: Some Old Hippie Caught Another Hippie Tripping On Acid.

2003 March 5, “Mnemonic Devices” (chapter 9), in Marcia L. Tate, editor, Worksheets Don't Grow Dendrites, SAGE Publications, →ISBN, archived from the original on 2024-03-20, page 93:

"It's easier with a mnemonic," Molly says. "Like… Some Old Hippie Caught Another Hippie Tripping On Acid—"

2015 December 1, Eric Lindstrom, chapter 23, in Not If I See You First, Little, Brown Books For Young Readers, →ISBN, archived from the original on 2024-03-19:

[…] I thought my mastery of sines, cosines, and tangents—Some Old Hippie Caught Another Hippie Tripping On Acid—might elevate me to another level of intellectual superiority in my high school; […]

2022 September, Jill Christman, “The Googly Eye”, in If This Were Fiction, archived from the original on 2024-03-20, page 92:

(trigonometry, humorous) A mnemonic used to help people remember the different trigonometric functions: sine is opposite over hypotenuse; cosine is adjacent over hypotenuse; and tangent is opposite over adjacent.