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The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler (1748).
The trigonometric functions, as the name suggests, are of crucial importance in trigonometry, mainly because of the following two results. Law of sines. The law of sines states that for an arbitrary triangle with sides a, b, and c and angles opposite those sides A, B and C: