Curve of the sine function

Topic:
Sine

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Move the point P on the trigonometric circle. The point N has abscissa α and ordinate sin(α). The resulting curve is the graphical representation of the sine function on [0;2π].

Courbe de la fonction sinus

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What happens to α when P makes more than one turn? How does the curve behave then? What if P turns in the nontrigonometric direction?