According to Math experts, Hipparchus, Menelaus, and Ptolemy are responsible for developing Greek trigonometry for the purposes of studying differences in shapes of the planets, sun and moon. By observing the shapes of each, they were able to determine the ratios and areas of each one.
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Hipparchus
About 100 b.c., during the period of the Alexandrian Greeks, the Greek astronomer Hipparchus developed what is today called spherical trigonometry. The Greek astronomers used spherical trigonometry to determine the time of day, direction of motion, and the positions of ships or reference points. Greek trigonometry flourished in the following centuries, reaching its highest point with the astronomer Menelaus (first century a.d.) and his successor, Ptolemy. Following the decline of Greek civilization about 640 a.d., little progress occurred until the advancement of science and mathematics recommenced during the Renaissance, beginning approximately in 1400.
According to recent (August 2017) research by the University of New South Wales, it was an unknown mathematician (or mathematicians) in Babylon. They produced a tablet, known as Plimpton 322, which contains tables of trig ration. This was some 1500 years before the Greek astronomer Hipparchus who, until now, was regarded the father of trigonometry. Thus, the Babylonian(s) may have been the first two astronomers - their identities are not recorded.
According to recent (August 2017) research by the University of New South Wales, it was an unknown mathematician (or mathematicians) in Babylon. They produced a tablet, known as Plimpton 322, which contains tables of trig ration. This was some 1500 years before the Greek astronomer Hipparchus who, until now, was regarded the father of trigonometry. Thus, the Babylonian(s) may have been the first two astronomers - their identities are not recorded.