Search results
Results from the WOW.Com Content Network
The legs of the two right triangles with hypotenuse on the ray defining the angles are of length √ 2 times the circular and hyperbolic functions. The hyperbolic angle is an invariant measure with respect to the squeeze mapping, just as the circular angle is invariant under rotation. [23] The Gudermannian function gives a direct relationship ...
Differentiation of integrals – Problem in mathematics; Differentiation under the integral sign – Differentiation under the integral sign formula; Hyperbolic functions – Collective name of 6 mathematical functions; Inverse hyperbolic functions – Mathematical functions; Inverse trigonometric functions – Inverse functions of sin, cos ...
Examples of functions that are not entire include the square root, the logarithm, the trigonometric function tangent, and its inverse, arctan. For these functions the Taylor series do not converge if x is far from b. That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor ...
The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. For example, the derivative of the sine function is written sin ′ ( a ) = cos( a ), meaning that the rate of change of sin( x ) at a particular angle x = a is given ...
The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.
As with other properties shared between the trigonometric functions and the hyperbolic functions, it is possible to use hyperbolic identities to construct a similar form of the substitution, = : sinh x = 2 t 1 − t 2 , cosh x = 1 + t 2 1 − t 2 , and d x = 2 1 − t 2 d t . {\displaystyle \sinh x={\frac {2t}{1-t^{2}}},\quad \cosh x ...
CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.