What kind of trigonometry appears in the Almagest?

The trigonometry found in the Almagest is based on the construction of a table of chords. Rather than using modern trigonometric functions, Ptolemy calculated the length of a chord in a circle as a function of the central angle that subtends it, for angles ranging from 0° to 180° at intervals of one-half degree.1

Because Ptolemy utilized the Babylonian sexagesimal (base 60) system, he performed these computations using a standard circle with a radius of $r=60$ units. This resulted in the formula $c=120\sin \frac{A}{2}$, where $c$ is the chord length and $A$ is the arc width. Consequently, this table functioned essentially as a table of sines, allowing for the calculation of planetary positions and other celestial phenomena. This mathematical mastery was essential for Ptolemy to develop his geocentric model of the universe.12