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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 trig word in the function stands for the trig function you have, either sine, cosine, tangent, or cotangent. The A stands for the amplitude of the function, or how high the function gets. The B value is the one you use to calculate your period.