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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.
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.
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You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
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).
In the diagram, such a circle is tangent to the hyperbola xy = 1 at (1,1). The yellow sector depicts an area and angle magnitude. The yellow sector depicts an area and angle magnitude. Similarly, the yellow and red regions together depict a hyperbolic sector with area corresponding to hyperbolic angle magnitude.
Examples of the application of the logistic S-curve to the response of crop yield (wheat) to both the soil salinity and depth to water table in the soil are shown in modeling crop response in agriculture. In artificial neural networks, sometimes non-smooth functions are used instead for efficiency; these are known as hard sigmoids.
The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer.Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection.