Basics of Trigonometry

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Trigonometry is a branch of mathematics that deals with sides and angles of a triangle. It has many identities. These identities are commonly used for writing different types of trigonometric expressions.

Sumerian astronomers studied measures of angles by dividing a complete angle in 360 equal parts. Hellenistic mathematicians, like Euclid and Archimedes, studied properties of chords and inscribed angles inside a circle. They also proved theorems similar to the modern trigonometric formulae. In his book titled Almagest, Ptolemy displayed complete table of trigonometric table of chords. Indian mathematician Aryabhata, as depicted in the book titled Surya Siddhanta[5], compiled modern sine convention for the first time during 5th Century A.D. Greek Almagest written by Ptolemy was translated in English and through that work trigonometry entered Europe.

Trigonometric Ratios

Trigonometric ratios are the ratios between edges of a right triangle.

Sine function (sin), defined as the ratio of the side opposite the angle to the hypotenuse.

Cosine function (cos), defined as the ratio of the adjacent leg (the side of the triangle joining the angle to the right angle) to the hypotenuse.

-- There are many more in this volume.