Search results
Results From The WOW.Com Content Network
So the inverse of a circle is the same circle if and only if it intersects the unit circle at right angles. To summarize and generalize this and the previous section: The inverse of a line or a circle is a line or a circle. If the original curve is a line then the inverse curve will pass through the center of inversion.
P ' is the inverse of P with respect to the circle. To invert a number in arithmetic usually means to take its reciprocal. A closely related idea in geometry is that of "inverting" a point. In the plane, the inverse of a point P with respect to a reference circle (Ø) with center O and radius r is a point P ', lying on the ray from O through P ...
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.
Download QR code; Print/export ... Unit circle; Laws and theorems; Sines; ... Ebook version, in PDF format, full text presented. Trigonometry by Alfred Monroe Kenyon ...
Ordinary trigonometry studies triangles in the Euclidean plane .There are a number of ways of defining the ordinary Euclidean geometric trigonometric functions on real numbers, for example right-angled triangle definitions, unit circle definitions, series definitions [broken anchor], definitions via differential equations [broken anchor], and definitions using functional equations.
The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle: For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord).
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Cayley transform of upper complex half-plane to unit disk. On the upper half of the complex plane, the Cayley transform is: [1] [2] = +.Since {,,} is mapped to {,,}, and Möbius transformations permute the generalised circles in the complex plane, maps the real line to the unit circle.