The word trigonometry derives from the Greek: "trigono" for triangle (three angles), and "metron" for measure. Trigonometry is the branch of mathematics which deals with the relations of sides and angles of triangles and with the relations among special functions associated with any angle.

Trigonometry was developed by ancient cultures as a tool to help with the precise mapping of the apparent motion of stars and planets through the sky, and with the prediction of celestial phenomena (faces of the moon, eclipses, equinoxes) with important effects on Earth. As such, the spherical trigonometry (the study of spherical triangles on the surface of the "celestial sphere", and which have arcs of circumferences for sides), came first into existence.

Although spherical trigonometry is much more complex than planar trigonometry because of the curvatures involved, it preceded the latter due to its astronomical interest.

The Greek mathematician Hipparchus of Rhodes (190-120 BC), who spent most of his life in the city of Alexandria, is considered the founder of trigonometry, since he produced the first tables of chords to be referenced in recorded history.

In geometry, a chord is the segment that joins any two points in a circumference, and more generically on any curve. The figure on the left shows a chord as the segment between points A and B on the circumference. The portions of circumference with A and B as starting and ending points, are called arcs of the circumference. The space subtended between the radii that joins the center of the circle with points A and B is called: "angle". As shown in the animation, with the given points A and B on the circumference and the center of the circle, two angles are defined, one much larger than the other, but both sharing the same chord.

The first tables produced by Hipparchus were for astronomical use, and consisted of twelve books, which unfortunately were lost. Only references to his work are found in documents by other mathematicians and astronomers. He was the first geometer to introduce the division of the circle in 360 equal angle sectors. Several books of chords in spherical and planar trigonometry were written by other astronomers and mathematicians in the following centuries.

Hipparchus

Ptolomy

Vatican copy of the Almagest

Ptolomy (100-178 AD) built very complete tables of chords at intervals of 1/2 of a degree. Using Hipparchus' technique of dividing the circle in 360 equal sectors, and using the chords of the circle to construct the 360 sides of the inscribed regular polygon, he derived an approximation for the value of the number pi: