Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships. Trigonometry has applications in both pure mathematics and in applied mathematics, where it is essential in many branches of science and technology.
It is usually taught in secondary schools either as a separate course or as part of a precalculus course.
Trigonometry is informally called "trig" or "trigo. A branch of trigonometry, called spherical trigonometry, studies triangles on spheresand is important in astronomy and navigation. Trigonometry was developed for use in sailing as a navigation method used with astronomy. The common practice of measuring angles in degrees, minutes and seconds comes from the Babylonian 's base sixty system of numeration. "Cos sin tan relationships dating" first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus  c.
Ptolemy further developed trigonometric calculations c. The ancient Sinhalese in Sri Lankawhen 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 B.
The Indian mathematician Aryabhata ingave 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 inused an interpolation formula to compute values of sines, up to the second order of the Newton -Stirling interpolation formula. Also in the late tenth and early eleventh centuries, the Egyptian astronomer Ibn Yunus performed many careful trigonometric calculations and demonstrated the formula.
Khayyam solved the cubic equation 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 inalong with some sine and cosine formulae. Bhaskara also developed spherical trigonometry. The thirteenth century Persian mathematician Nasir al-Din Tusi, along with Bhaskara, was probably the first to treat trigonometry as a distinct mathematical discipline.
Nasir Cos sin tan relationships dating 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 fourteenth 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 which may have coined the word "trigonometry" itself. If one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to degrees.
The two acute angles therefore add up Cos sin tan relationships dating 90 degrees: They are complementary angles. The shape of a right triangle is completely determined, up to similarity, by the angles. This means that once one of the other angles is known, the ratios of the various sides are always the same regardless of the overall size of the triangle.