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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).
Defining relations for tangent, cotangent, secant, and cosecant in terms of sine and cosine. The Pythagorean formula for sines and cosines. This is probably the most important trig identity. Identities expressing trig functions in terms of their complements. There's not much to these. Each of the six trig functions is equal to its co-function evaluated at the complementary angle. Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2 Ï while tangent and cotangent have period Ï. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions.