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The notations for the five remaining trigonometric functions were introduced shortly thereafter.

During the Middle Ages, while Europe was plunged into darkness, the torch of learning was kept alive by Jewish scholars living in Spain, Mesopotamia, and Persia.

This is actually the “run-to-rise” ratio of the pyramid in question—in effect, the cotangent of the angle between the base and face.

It shows that the Egyptians had at least some knowledge of the numerical relations in a triangle, a kind of “proto-trigonometry.”) was the first to construct a table of values for a trigonometric function.

As an astronomer, Hipparchus was mainly interested in spherical triangles, such as the imaginary triangle formed by three stars on the celestial sphere, but he was also familiar with the basic formulas of plane trigonometry.

independent of the size of the triangle, and calculated values were tabulated for many angles before computers made trigonometry tables obsolete.

Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures.astronomy, mapmaking, surveying, and artillery range finding.

The first table of tangents and cotangents was constructed around 860 by Ḥabash al-Ḥāsib (“the Calculator”), who wrote on astronomy and astronomical instruments. Based on this rule he constructed a “table of shadows”—essentially a table of cotangents—for each degree from 1° to 90°.

It was through al-Bāttāni’s work that the Hindu half-chord function—equivalent to the modern sine—became known in Europe.) in which Menelaus developed the spherical equivalents of Euclid’s propositions for planar triangles.