Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles and the calculations of trigonometric functions. It has many applications in fields like navigation, surveying, physics, engineering and more. Some key aspects covered are the definitions of trigonometric functions like sine, cosine and tangent; common trigonometric identities; formulae for calculating unknown sides and angles of triangles; and the history of trigonometry dating back to ancient Greek and Indian mathematicians.

1. Trigonometry
“Trig” redirects here. For other uses, see Trig (disam-
biguation).
Trigonometry (from Greek trigōnon, “triangle” and
The Canadarm2 robotic manipulator on the International Space
Station is operated by controlling the angles of its joints. Calcu-
lating the final position of the astronaut at the end of the arm
requires repeated use of trigonometric functions of those angles.
metron, “measure”[1]
) is a branch of mathematics that
studies relationships involving lengths and angles of
triangles. The field emerged in the Hellenistic world dur-
ing the 3rd century BC from applications of geometry to
astronomical studies.[2]
The 3rd-century astronomers first noted that the lengths
of the sides of a right-angle triangle and the angles be-
tween those sides have fixed relationships: that is, if at
least the length of one side and the value of one angle
is known, then all other angles and lengths can be de-
termined algorithmically. These calculations soon came
to be defined as the trigonometric functions and today
are pervasive in both pure and applied mathematics: fun-
damental methods of analysis such as the Fourier trans-
form, for example, or the wave equation, use trigono-
metric functions to understand cyclical phenomena across
many applications in fields as diverse as physics, mechan-
ical and electrical engineering, music and acoustics, as-
tronomy, ecology, and biology. Trigonometry is also the
foundation of surveying.
Trigonometry is most simply associated with planar right-
angle triangles (each of which is a two-dimensional tri-
angle with one angle equal to 90 degrees). The appli-
cability to non-right-angle triangles exists, but, since any
non-right-angle triangle (on a flat plane) can be bisected
to create two right-angle triangles, most problems can be
reduced to calculations on right-angle triangles. Thus
the majority of applications relate to right-angle trian-
gles. One exception to this is spherical trigonometry, the
study of triangles on spheres, surfaces of constant posi-
tive curvature, in elliptic geometry (a fundamental part
of astronomy and navigation). Trigonometry on surfaces
of negative curvature is part of hyperbolic geometry.
Trigonometry basics are often taught in schools, either as
a separate course or as a part of a precalculus course.
1 History
Main article: History of trigonometry
Sumerian astronomers studied angle measure, using a di-
Hipparchus, credited with compiling the first trigonometric table,
is known as “the father of trigonometry”.[3]
vision of circles into 360 degrees.[4]
They, and later the
Babylonians, studied the ratios of the sides of similar tri-
angles and discovered some properties of these ratios but
did not turn that into a systematic method for finding sides
and angles of triangles. The ancient Nubians used a sim-
ilar method.[5]
In the 3rd century BCE, Hellenistic Greek mathemati-
cians (such as Euclid and Archimedes) studied the prop-
erties of chords and inscribed angles in circles, and they
proved theorems that are equivalent to modern trigono-
1

2. 2 2 OVERVIEW
metric formulae, although they presented them geomet-
rically rather than algebraically. In 140 BC Hipparchus
gave the first tables of chords, analogous to modern
tables of sine values, and used them to solve prob-
lems in trigonometry and spherical trigonometry.[6]
In the
2nd century AD the Greco-Egyptian astronomer Ptolemy
printed detailed trigonometric tables (Ptolemy’s table
of chords) in Book 1, chapter 11 of his Almagest.[7]
Ptolemy used chord length to define his trigonometric
functions, a minor difference from the sine convention
we use today.[8]
(The value we call sin(θ) can be found
by looking up the chord length for twice the angle of
interest (2θ) in Ptolemy’s table, and then dividing that
value by two.) Centuries passed before more detailed
tables were produced, and Ptolemy’s treatise remained
in use for performing trigonometric calculations in as-
tronomy throughout the next 1200 years in the medieval
Byzantine, Islamic, and, later, Western European worlds.
The modern sine convention is first attested in the Surya
Siddhanta, and its properties were further documented
by the 5th century (CE) Indian mathematician and as-
tronomer Aryabhata.[9]
These Greek and Indian works
were translated and expanded by medieval Islamic math-
ematicians. By the 10th century, Islamic mathemati-
cians were using all six trigonometric functions, had tab-
ulated their values, and were applying them to prob-
lems in spherical geometry. At about the same time,
Chinese mathematicians developed trigonometry inde-
pendently, although it was not a major field of study
for them. Knowledge of trigonometric functions and
methods reached Western Europe via Latin translations
of Ptolemy’s Greek Almagest as well as the works of
Persian and Arabic astronomers such as Al Battani and
Nasir al-Din al-Tusi.[10]
One of the earliest works on
trigonometry by a northern European mathematician is
De Triangulis by the 15th century German mathemati-
cian Regiomontanus, who was encouraged to write, and
provided with a copy of the Almagest, by the Byzantine
Greek scholar cardinal Basilios Bessarion with whom he
lived for several years.[11]
At the same time another trans-
lation of the Almagest from Greek into Latin was com-
pleted by the Cretan George of Trebizond.[12]
Trigonom-
etry was still so little known in 16th-century northern Eu-
rope that Nicolaus Copernicus devoted two chapters of
De revolutionibus orbium coelestium to explain its basic
concepts.
Driven by the demands of navigation and the grow-
ing need for accurate maps of large geographic
areas, trigonometry grew into a major branch of
mathematics.[13]
Bartholomaeus Pitiscus was the first to
use the word, publishing his Trigonometria in 1595.[14]
Gemma Frisius described for the first time the method
of triangulation still used today in surveying. It was
Leonhard Euler who fully incorporated complex num-
bers into trigonometry. The works of the Scottish math-
ematicians James Gregory in the 17th century and Colin
Maclaurin in the 18th century were influential in the de-
velopment of trigonometric series.[15]
Also in the 18th
century, Brook Taylor defined the general Taylor se-
ries.[16]
2 Overview
Main article: Trigonometric function
If one angle of a triangle is 90 degrees and one of the
A
B
C
c
a
b
Adjacent
Opposite
Hypotenuse
In this right triangle: sin A = a/ c; cos A = b/ c; tan A = a/ b.
other angles is known, the third is thereby fixed, because
the three angles of any triangle add up to 180 degrees.
The two acute angles therefore add up to 90 degrees: they
are complementary angles. The shape of a triangle is
completely determined, except for similarity, by the an-
gles. Once the angles are known, the ratios of the sides
are determined, regardless of the overall size of the trian-
gle. If the length of one of the sides is known, the other
two are determined. These ratios are given by the follow-
ing trigonometric functions of the known angle A, where
a, b and c refer to the lengths of the sides in the accom-
panying figure:
• Sine function (sin), defined as the ratio of the side
opposite the angle to the hypotenuse.
sin A =
opposite
hypotenuse
=
a
c
.
• Cosine function (cos), defined as the ratio of the
adjacent leg to the hypotenuse.
cos A =
adjacent
hypotenuse
=
b
c
.
• Tangent function (tan), defined as the ratio of the
opposite leg to the adjacent leg.

3. 2.2 Mnemonics 3
tan A =
opposite
adjacent
=
a
b
=
a
c
∗
c
b
=
a
c
/
b
c
=
sin A
cos A
.
The hypotenuse is the side opposite to the 90 degree an-
gle in a right triangle; it is the longest side of the trian-
gle and one of the two sides adjacent to angle A. The
adjacent leg is the other side that is adjacent to an-
gle A. The opposite side is the side that is opposite to
angle A. The terms perpendicular and base are some-
times used for the opposite and adjacent sides respec-
tively. Many people find it easy to remember what sides
of the right triangle are equal to sine, cosine, or tangent,
by memorizing the word SOH-CAH-TOA (see below un-
der Mnemonics).
The reciprocals of these functions are named the cose-
cant (csc or cosec), secant (sec), and cotangent (cot),
respectively:
csc A =
1
sin A
=
hypotenuse
opposite
=
c
a
,
sec A =
1
cos A
=
hypotenuse
adjacent
=
c
b
,
cot A =
1
tan A
=
adjacent
opposite
=
cos A
sin A
=
b
a
.
The inverse functions are called the arcsine, arccosine,
and arctangent, respectively. There are arithmetic re-
lations between these functions, which are known as
trigonometric identities. The cosine, cotangent, and cose-
cant are so named because they are respectively the sine,
tangent, and secant of the complementary angle abbrevi-
ated to “co-".
With these functions one can answer virtually all ques-
tions about arbitrary triangles by using the law of sines
and the law of cosines. These laws can be used to com-
pute the remaining angles and sides of any triangle as soon
as two sides and their included angle or two angles and a
side or three sides are known. These laws are useful in all
branches of geometry, since every polygon may be de-
scribed as a finite combination of triangles.
2.1 Extending the definitions
The above definitions only apply to angles between 0 and
90 degrees (0 and π/2 radians). Using the unit circle,
one can extend them to all positive and negative argu-
ments (see trigonometric function). The trigonometric
functions are periodic, with a period of 360 degrees or
2π radians. That means their values repeat at those in-
tervals. The tangent and cotangent functions also have a
shorter period, of 180 degrees or π radians.
The trigonometric functions can be defined in other ways
besides the geometrical definitions above, using tools
Fig. 1a – Sine and cosine of an angle θ defined using the unit
circle.
from calculus and infinite series. With these definitions
the trigonometric functions can be defined for complex
numbers. The complex exponential function is particu-
larly useful.
ex+iy
= ex
(cos y + i sin y).
See Euler’s and De Moivre’s formulas.
• Graphing process of y = sin(x) using a unit circle.
• Graphing process of y = csc(x), the reciprocal of
sine, using a unit circle.
• Graphing process of y = tan(x) using a unit circle.
2.2 Mnemonics
Main article: Mnemonics in trigonometry
A common use of mnemonics is to remember facts and
relationships in trigonometry. For example, the sine, co-
sine, and tangent ratios in a right triangle can be remem-
bered by representing them and their corresponding sides
as strings of letters. For instance, a mnemonic is SOH-
CAH-TOA:[17]
Sine = Opposite ÷ Hypotenuse
Cosine = Adjacent ÷ Hypotenuse
Tangent = Opposite ÷ Adjacent
One way to remember the letters is to sound them out
phonetically (i.e., SOH-CAH-TOA, which is pronounced
'so-kə-toe-uh' /soʊkəˈtoʊə/). Another method is to ex-
pand the letters into a sentence, such as "Some Old Hippy
Caught Another Hippy Trippin' On Acid”.[18]

4. 4 6 COMMON FORMULAE
2.3 Calculating trigonometric functions
Main article: Trigonometric tables
Trigonometric functions were among the earliest uses for
mathematical tables. Such tables were incorporated into
mathematics textbooks and students were taught to look
up values and how to interpolate between the values listed
to get higher accuracy. Slide rules had special scales for
trigonometric functions.
Today scientific calculators have buttons for calculating
the main trigonometric functions (sin, cos, tan, and some-
times cis and their inverses). Most allow a choice of an-
gle measurement methods: degrees, radians, and some-
times gradians. Most computer programming languages
provide function libraries that include the trigonometric
functions. The floating point unit hardware incorporated
into the microprocessor chips used in most personal com-
puters has built-in instructions for calculating trigonomet-
ric functions.[19]
3 Applications of trigonometry
Sextants are used to measure the angle of the sun or stars with re-
spect to the horizon. Using trigonometry and a marine chronome-
ter, the position of the ship can be determined from such measure-
ments.
Main article: Uses of trigonometry
There is an enormous number of uses of trigonometry and
trigonometric functions. For instance, the technique of
triangulation is used in astronomy to measure the distance
to nearby stars, in geography to measure distances be-
tween landmarks, and in satellite navigation systems. The
sine and cosine functions are fundamental to the theory of
periodic functions such as those that describe sound and
light waves.
Fields that use trigonometry or trigonometric functions
include astronomy (especially for locating apparent po-
sitions of celestial objects, in which spherical trigonom-
etry is essential) and hence navigation (on the oceans,
in aircraft, and in space), music theory, audio syn-
thesis, acoustics, optics, electronics, probability the-
ory, statistics, biology, medical imaging (CAT scans
and ultrasound), pharmacy, chemistry, number the-
ory (and hence cryptology), seismology, meteorology,
oceanography, many physical sciences, land surveying
and geodesy, architecture, image compression, phonetics,
economics, electrical engineering, mechanical engineer-
ing, civil engineering, computer graphics, cartography,
crystallography and game development.
4 Pythagorean identities
Identities are those equations that hold true for any value.
sin2
A + cos2
A = 1
(The following two can be derived from the first.)
sec2
A − tan2
A = 1
csc2
A − cot2
A = 1
5 Angle transformation formulae
sin(A ± B) = sin A cos B ± cos A sin B
cos(A ± B) = cos A cos B ∓ sin A sin B
tan(A ± B) =
tan A ± tan B
1 ∓ tan A tan B
cot(A ± B) =
cot A cot B ∓ 1
cot B ± cot A
6 Common formulae
Certain equations involving trigonometric functions are
true for all angles and are known as trigonometric identi-
ties. Some identities equate an expression to a different
expression involving the same angles. These are listed in
List of trigonometric identities. Triangle identities that
relate the sides and angles of a given triangle are listed
below.
In the following identities, A, B and C are the angles of
a triangle and a, b and c are the lengths of sides of the
triangle opposite the respective angles (as shown in the
diagram).

5. 6.3 Law of tangents 5
Triangle with sides a,b,c and respectively opposite angles A,B,C
6.1 Law of sines
The law of sines (also known as the “sine rule”) for an
arbitrary triangle states:
a
sin A
=
b
sin B
=
c
sin C
= 2R =
abc
2∆
,
where ∆ is the area of the triangle and R is the radius of
the circumscribed circle of the triangle:
R =
abc
√
(a + b + c)(a − b + c)(a + b − c)(b + c − a)
.
Another law involving sines can be used to calculate the
area of a triangle. Given two sides a and b and the angle
between the sides C, the area of the triangle is given by
half the product of the lengths of two sides and the sine
of the angle between the two sides:
Area = ∆ =
1
2
ab sin C.
6.2 Law of cosines
The law of cosines (known as the cosine formula, or the
“cos rule”) is an extension of the Pythagorean theorem to
arbitrary triangles:
c2
= a2
+ b2
− 2ab cos C,
or equivalently:
cos C =
a2
+ b2
− c2
2ab
.
O
θ
A
B
C
D E
F
1
sinsin
cvs
excsc
csc
cos versin exsec
sec
chord
cot
tan
All of the trigonometric functions of an angle θ can be con-
structed geometrically in terms of a unit circle centered at O.
The law of cosines may be used to prove Heron’s formula,
which is another method that may be used to calculate the
area of a triangle. This formula states that if a triangle has
sides of lengths a, b, and c, and if the semiperimeter is
s =
1
2
(a + b + c),
then the area of the triangle is:
Area = ∆ =
√
s(s − a)(s − b)(s − c) =
abc
4R
where R is the radius of the circumcircle of the triangle.
6.3 Law of tangents
The law of tangents:
a − b
a + b
=
tan
[1
2 (A − B)
]
tan
[1
2 (A + B)
]
6.4 Euler’s formula
Euler’s formula, which states that eix
= cos x + i sin x
, produces the following analytical identities for sine, co-
sine, and tangent in terms of e and the imaginary unit i:
sin x =
eix
− e−ix
2i
, cos x =
eix
+ e−ix
2
, tan x =
i(e−ix
− eix
)
eix + e−ix
7 See also
• Aryabhata’s sine table
• Generalized trigonometry

6. 6 10 EXTERNAL LINKS
• Lénárt sphere
• List of triangle topics
• List of trigonometric identities
• Rational trigonometry
• Skinny triangle
• Small-angle approximation
• Trigonometric functions
• Trigonometry in Galois fields
• Unit circle
• Uses of trigonometry
8 References
[1] “trigonometry”. Online Etymology Dictionary.
[2] R. Nagel (ed.), Encyclopedia of Science, 2nd Ed., The
Gale Group (2002)
[3] Boyer (1991). “Greek Trigonometry and Mensuration”.
A History of Mathematics. p. 162.
[4] Aaboe, Asger. Episodes from the Early History of As-
tronomy. New York: Springer, 2001. ISBN 0-387-
95136-9
[5] Otto Neugebauer (1975). A history of ancient mathemat-
ical astronomy. 1. Springer-Verlag. pp. 744–. ISBN
978-3-540-06995-9.
[6] Thurston, pp. 235–236.
[7] Toomer, G. J. (1998), Ptolemy’s Almagest, Princeton Uni-
versity Press, ISBN 0-691-00260-6
[8] Thurston, pp. 239–243.
[9] Boyer p. 215
[10] Boyer pp. 237, 274
[11] http://www-history.mcs.st-and.ac.uk/Biographies/
Regiomontanus.html
[12] N.G. Wilson, From Byzantium to Italy. Greek Studies in the
Italian Renaissance, London, 1992. ISBN 0-7156-2418-0
[13] Grattan-Guinness, Ivor (1997). The Rainbow of Mathe-
matics: A History of the Mathematical Sciences. W.W.
Norton. ISBN 0-393-32030-8.
[14] Robert E. Krebs (2004). Groundbreaking Scientific Exper-
iments, Inventions, and Discoveries of the Middle Ages and
the Renaissnce. Greenwood Publishing Group. pp. 153–.
ISBN 978-0-313-32433-8.
[15] William Bragg Ewald (2008). From Kant to Hilbert: a
source book in the foundations of mathematics. Oxford
University Press US. p. 93. ISBN 0-19-850535-3
[16] Kelly Dempski (2002). Focus on Curves and Surfaces. p.
29. ISBN 1-59200-007-X
[17] Weisstein, Eric W., “SOHCAHTOA”, MathWorld.
[18] A sentence more appropriate for high schools is “Some old
horse came a'hopping through our alley”. Foster, Jonathan
K. (2008). Memory: A Very Short Introduction. Oxford.
p. 128. ISBN 0-19-280675-0.
[19] Intel® 64 and IA-32 Architectures Software Developer’s
Manual Combined Volumes: 1, 2A, 2B, 2C, 3A, 3B and
3C (PDF). Intel. 2013.
9 Bibliography
• Boyer, Carl B. (1991). A History of Mathematics
(Second ed.). John Wiley & Sons, Inc. ISBN 0-
471-54397-7.
• Hazewinkel, Michiel, ed. (2001), “Trigonometric
functions”, Encyclopedia of Mathematics, Springer,
ISBN 978-1-55608-010-4
• Christopher M. Linton (2004). From Eudoxus to
Einstein: A History of Mathematical Astronomy .
Cambridge University Press.
• Weisstein, Eric W., “Trigonometric Addition For-
mulas”, MathWorld.
10 External links
• Khan Academy: Trigonometry, free online micro
lectures
• Trigonometry by Alfred Monroe Kenyon and Louis
Ingold, The Macmillan Company, 1914. In images,
full text presented.
• Benjamin Banneker’s Trigonometry Puzzle at
Convergence
• Dave’s Short Course in Trigonometry by David
Joyce of Clark University
• Trigonometry, by Michael Corral, Covers elemen-
tary trigonometry, Distributed under GNU Free
Documentation License

7. 7
11 Text and image sources, contributors, and licenses
11.1 Text
• Trigonometry Source: http://en.wikipedia.org/wiki/Trigonometry?oldid=663170707 Contributors: AxelBoldt, Zundark, Andre Engels,
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J.delanoy, Kimse, Trusilver, Rgoodermote, Ali, Tikiwont, Terrek, Lightcatcher, Ajmint, InternationalEducation, Krishnachandranvn, The
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Solar de Harmonics, Shshshsh, NinjaTerdle, JavierMC, Kiwiinoz77, Vinsfan368, CP TTD, Xiahou, Squids and Chips, Idioma-bot, Xnuala,
Lights, X!, Lord of Conquest, Deor, Rmirester, VolkovBot, ABF, Pleasantville, Jeff G., JohnBlackburne, Nburden, TheOtherJesse, Amishb-
hadeshia, Barneca, Sześćsetsześćdziesiątsześć, NYDirk, Ampersandfrabjous(mark), Philip Trueman, TXiKiBoT, Malinaccier, Editor plus,
Technopat, Xerxesnine, Miranda, Anonymous Dissident, UYHAT238, Clark Kimberling, Anna Lincoln, DennyColt, Corvus cornix, Ab-
dullais4u, LeaveSleaves, Rustysrfbrds99, Chriscooperlondon, Cremepuff222, Thiefer, R0ssar00, Isis4563, CO, Larklight, Enigmaman,
ImmortalKnight, SmileToday, Enviroboy, Sallz0r, Sylent, Spinningspark, Insanity Incarnate, Dmcq, AlleborgoBot, Praefectorian, Symane,
W4chris, Hughey, Ken Kuniyuki, Kbrose, Netopalis, Minestrone Soup, SieBot, Coffee, Dusti, Nubiatech, Tiddly Tom, Work permit, Scar-
ian, Sawjansee, BotMultichill, Dtreed, Viskonsas, Caltas, Yintan, Bentogoa, Tiptoety, Arbor to SJ, CutOffTies, Nuttycoconut, KPH2293,
Bagatelle, Hobartimus, OKBot, Infemous, Kaycooksey, Randomblue, Superbeecat, Nic bor, Wahrmund, Besimmons, 3rdAlcove, Ex-
plicit, Faithlessthewonderboy, Owenshahim, Church, Martarius, DocRushing, ClueBot, NickCT, Kl4m, GorillaWarfare, Alpha Beta Ep-
silon, Fyyer, The Thing That Should Not Be, Helenabella, TrigWorks, Abhinav, Aditibhatia29, Blocklayer, R000t, Utoddl, LarnerGAL,
Crumbinator, Ramiz.Ibrahim, Excirial, Alexbot, Abrech, ParisianBlade, Prancibaldfpants, Echion2, NuclearWarfare, CylonSix, Cenarium,
Aurora2698, Jotterbot, Eustress, Razorflame, Dekisugi, DatDoo, BOTarate, Thingg, Kruusamägi, Ubardak, DumZiBoT, Kiensvay, Crazy
Boris with a red beard, Bgreise24, BendersGame, Rankiri, Jovianeye, Duncan, Avoided, SilvonenBot, NellieBly, Dinosaursrule42, Sw8511,
Matt5215, HexaChord, Simon12345, Addbot, Cxz111, Wigert, Physprob, Tcncv, Landon1980, Captain-tucker, AkhtaBot, Georgebush3,
Jncraton, Fieldday-sunday, Catherinemandot, CanadianLinuxUser, Mohammed farag, Cst17, Mohamed Magdy, MrOllie, Glane23, Favo-
nian, Kyle1278, 5 albert square, Sirturtle1990, Squandermania, Manorupa108, Ehrenkater, Timyxp, Tide rolls, Zorrobot, TeH nOmInAtOr,
Quantumobserver, HerculeBot, Crt, Cooookie3001, Ben Ben, Math Champion, Luckas-bot, Yobot, Tohd8BohaithuGh1, Senator Palpatine,
Gobbleswoggler, Mmxx, Ajh16, Goodberry, Wikihelper100, AnomieBOT, IRP, Proevaholic, AdjustShift, Kingpin13, Halfs, Materialsci-
entist, Citation bot, Akilaa, E2eamon, Frankenpuppy, ArthurBot, Xqbot, Sathimantha, TinucherianBot II, Techsmoke15, JimVC3, Nas-
nema, Ksagittariusr, Tyrol5, Gap9551, Sabio101, Omnipaedista, RibotBOT, Charvest, Doulos Christos, WhizzWizard, Raulshc, Sophus
Bie, GhalyBot, Shadowjams, Skepticalmouse, Nfgsurf7, Griffinofwales, Prari, FrescoBot, Tobby72, Pepper, Dan1232112321, Wikipe-tan,
Oldlaptop321, Routerone, Biscuit555, Rigaudon, Swaying tree, TheStudentRoom, Jamesooders, Wireless Keyboard, HamburgerRadio, 4pi,
Cobness, Dirtyasianmen, Watsup101, Pinethicket, I dream of horses, Boulaur, Hendvi, Kiefer.Wolfowitz, 01000100 W 01000010, Calmer
Waters, A8UDI, POOEATZA, Jschnur, Impala2009, Nosoup4uNOOB, SpaceFlight89, Σ, Rohitphy, Prin09, Maheshnathwani, Dude1818,
Dysfunktionall, Ykhatana1, FoxBot, TobeBot, PorkHeart, Vrenator, Leebian, Diannaa, Ammodramus, Pedro999999999, Stupid geometric
shapes, Uber smart man, Sideways713, TjBot, Beyond My Ken, Hajatvrc, Saulth, Balph Eubank, Ctdpmet2, Jack Schlederer, Onef9day,
EmausBot, Stryn, Immunize, Gfoley4, Ibbn, NotAnonymous0, Wikipelli, Pjboonstra, MonoALT, Sardar0987, JSquish, Fæ, Nicajele-
junsutuc, Rosswante, Monterey Bay, Openstrings, Mlpearc Public, Colin.campbell.27, L Kensington, Donner60, Chewings72, Herebo,
ChuispastonBot, Nicepepper, PaulAg54, ClueBot NG, Smtchahal, Kingofpoptarts, Mblum116, Arnavmishra2050, Gareth Griffith-Jones,
Gvsip, Wcherowi, Zg001, Movses-bot, Churrrp, Krishnan.adarsh, Muon, Marechal Ney, Widr, Jorgenev, Helpful Pixie Bot, Thisthat2011,

8. 8 11 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES
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