Unit circle

In mathematics, a unit circle is a circle with unit radius, i.e., a circle whose radius is 1. Frequently, especially in trigonometry, "the" unit circle is the circle of radius 1 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 ball.

Related Topics:
Mathematics - Circle - Unit - Radius - Trigonometry - Cartesian coordinate system - Unit ball

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If (x, y) is a point on the unit circle in the first quadrant, 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

Related Topics:
Right triangle - Pythagorean theorem

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:x^2 + y^2 = 1 ,!

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Since x2 = (−x)2 for all x, and since the reflection of any point on the unit circle about the x- or y-axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not just those in the first quadrant.

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One may also use other notions of "distance" to define other "unit circles"; see the article on normed vector space for examples.

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