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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).
Create three parametric functions. The point on one of the functions will travel like the second hand on a clock. The point on the second function will travel like the minute hand on a clock. The point on the third function will travel like the hour hand on a clock.