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Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [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 tangent line to the unit circle at the point A, is perpendicular to , and intersects the y - and x-axes at points = (,) and = (,). The coordinates of these points give the values of all trigonometric functions for any arbitrary real value of θ in the following manner.
English: All of the six trigonometric functions of an arbitrary angle θ can be defined geometrically in terms of a unit circle centred at the origin of a Cartesian coordinate plane.
Penny graphs have also been called unit coin graphs, [2] because they are the coin graphs formed from unit circles. [1] If each vertex is represented by a point at the center of its circle, then two vertices will be adjacent if and only if their distance is the minimum distance among all pairs of vertices.
The circle packing theorem [2] states that every planar graph can be represented as a contact graph of circles. The contact graphs of unit circles are called penny graphs. [3] Representations as contact graphs of triangles, [4] rectangles, [5] squares, [6] line segments, [7] or circular arcs [8] have also been studied.
Radial lines (those running through the pole) are represented by the equation =, where is the angle of elevation of the line; that is, = , where is the slope of the line in the Cartesian coordinate system. The non-radial line that crosses the radial line = perpendicularly at the point (,) has the equation = ().
No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle. The geometrical figure of a circle and both tangent lines likewise has a reflection symmetry about the radial axis joining P to the center point O of ...
The following outline is provided as an overview of and topical guide to trigonometry: . Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles.