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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).
By the 10th century, Muslim mathematicians had developed and applied the theory of trigonometric functions -- sine, cosine, and tangent -- as well as spherical trigonometry. They used symbols to describe the binomial theorem, and used decimals to express fractions that aided accurate solution of complex problems.