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                                          UNIT-CIRCLE.

In mathematics, a unit circle is a circle with unit radius. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S1; the generalization to higher dimensions is the unit sphere.

If (x, y) is a point on the unit circle's circumference, then |x| and |y| are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and y satisfy the equation
x² + y² = 1.

 

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