Search results
Results From The WOW.Com Content Network
Under the above conditions, there exists a solution to the problem for any given set of data points {x k, y k} as long as N, the number of data points, is not larger than the number of coefficients in the polynomial, i.e., N ≤ 2K+1 (a solution may or may not exist if N>2K+1 depending upon the particular set of data points).
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the ...
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A.As is shown, H and A are almost the same length, meaning cos θ is close to 1 and θ 2 / 2 helps trim the red away.
In probability theory and statistics, the raised cosine distribution is a continuous probability distribution supported on the interval [, +].The probability density function (PDF) is
This can be seen in the following tables, the left of which shows Newton's method applied to the above f(x) = x + x 4/3 and the right of which shows Newton's method applied to f(x) = x + x 2. The quadratic convergence in iteration shown on the right is illustrated by the orders of magnitude in the distance from the iterate to the true root (0,1 ...
The analog of the Pythagorean trigonometric identity holds: [2] + = If X is a diagonal matrix, sin X and cos X are also diagonal matrices with (sin X) nn = sin(X nn) and (cos X) nn = cos(X nn), that is, they can be calculated by simply taking the sines or cosines of the matrices's diagonal components.
Octave (aka GNU Octave) is an alternative to MATLAB. Originally conceived in 1988 by John W. Eaton as a companion software for an undergraduate textbook, Eaton later opted to modify it into a more flexible tool. Development began in 1992 and the alpha version was released in 1993. Subsequently, version 1.0 was released a year after that in 1994.