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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.
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.
Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.
English: This is a graphical construction of the various trigonometric functions from a chord AD (angle θ) of the unit circle centered at O. In addition to the modern trigonometric functions sin (sine), cos (cosine), tan (tangent), cot (cotangent), sec (secant), and csc (cosecant), the diagram also includes a few trigonometric functions that have fallen into disuse: chord, versin (versine or ...
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English: Some common angles (multiples of 30 and 45 degrees) and the corresponding sine and cosine values shown on the Unit circle. The angles (θ) are given in degrees and radians, together with the corresponding intersection point on the unit circle, (cos θ, sin θ).
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