Trigonometry was probably developed for use in sailing as a
navigation method used with astronomy.[2] The origins of
trigonometry can be traced to the civilizations of ancient Egypt,
Mesopotamia and the Indus Valley, more than 4000 years
ago.[citation needed] The common practice of measuring angles in
degrees, minutes and seconds comes from the Babylonian's base sixty
system of numeration. The Sulba Sutras written in India, between
800 BC and 500 BC, correctly computes the sine of (=45°) as in a
procedure for "circling the square" (i.e., constructing the
inscribed circle).[citation needed]
The first recorded use of trigonometry came from the Hellenistic
mathematician Hipparchus[1] circa 150 BC, who compiled a
trigonometric table using the sine for solving triangles. Ptolemy
further developed trigonometric calculations circa 100 AD.
The ancient Sinhalese in Sri Lanka, when constructing reservoirs
in the Anuradhapura kingdom, used trigonometry to calculate the
gradient of the water flow. Archeological research also provides
evidence of trigonometry used in other unique hydrological
structures dating back to 4 BC.[3]
The Indian mathematician Aryabhata in 499, gave tables of half
chords which are now known as sine tables, along with cosine
tables. He used zya for sine, kotizya for cosine, and otkram zya
for inverse sine, and also introduced the versine. Another Indian
mathematician, Brahmagupta in 628, used an interpolation formula to
compute values of sines, up to the second order of the
Newton-Stirling interpolation formula.
In the 10th century, the Persian mathematician and astronomer
Abul Wáfa introduced the tangent function and improved methods of
calculating trigonometry tables. He established the angle addition
identities, e.g. sin (a + b), and discovered the sine formula for
spherical geometry:
Also in the late 10th and early 11th centuries, the Egyptian
astronomer Ibn Yunus performed many careful trigonometric
calculations and demonstrated the formula
.
Indian mathematicians were the pioneers of variable computations
algebra for use in astronomical calculations along with
trigonometry. Lagadha (circa 1350-1200 BC) is the first person
thought to have used geometry and trigonometry for astronomy, in
his Vedanga Jyotisha.
Persian mathematician Omar Khayyám (1048-1131) combined
trigonometry and approximation theory to provide methods of solving
algebraic equations by geometrical means. Khayyam solved the cubic
equation x3 + 200x = 20x2 + 2000 and found a positive root of this
cubic by considering the intersection of a rectangular hyperbola
and a circle. An approximate numerical solution was then found by
interpolation in trigonometric tables.
Detailed methods for constructing a table of sines for any angle
were given by the Indian mathematician Bhaskara in 1150, along with
some sine and cosine formulae. Bhaskara also developed spherical
trigonometry.
The 13th century Persian mathematician Nasir al-Din Tusi, along
with Bhaskara, was probably the first to treat trigonometry as a
distinct mathematical discipline. Nasir al-Din Tusi in his Treatise
on the Quadrilateral was the first to list the six distinct cases
of a right angled triangle in spherical trigonometry.
In the 14th century, Persian mathematician al-Kashi and Timurid
mathematician Ulugh Beg (grandson of Timur) produced tables of
trigonometric functions as part of their studies of astronomy.
The mathematician Bartholemaeus Pitiscus published an
influential work on trigonometry in 1595 which may have coined the
word "trigonometry".
