Trigonometric functions

        In the ancient times mathematicians described the relation between the angle formed by two radii of a circle and the length of the line segment determined by the endpoints of the two radii on the circle.

        Antien Greek mathematicians Hipparchus (166-125 BC) and about hundred years later Menelaus of Alexandria (famous for his earliest theorems on spherical trigonometry) measured the lenght of the chords in the above configuration for different angles and calculated their ratio to the circle radius. These measures of chords were in fact double values of our nowadays sine function.

        These calculations were published in the famous book "Almagest - Syntaxis mathematica" by Greek Ptolemy Claudius (2^nd century AD), where tables with chord measures for angles within 0 to 360 degrees in the 30-minute steps order appeared together with a clear description of just how the table was constructed.

        In the 9^th century, Arabic mathematicians started to use halfs of the presented numbers only, that means half-sections. The name "sine" appeared in the 12^th century, after a non-proper translation of the arabic word "el dzeib", which means section - intersection, but also a bay.

        Later on, trigonometric functions became important in the spherical geometry that formed the bases of the celestial mechanics. Astronomical coordinate system is used to define the position of the celestial objects on the celestial sphere using spherical curve-like triangles and spherical trigonometry.