Trigonometric functions of inverse trigonometric functions are tabulated below. One application is the definition of inverse trigonometric functions. The algorithm is very similar to that provided above for computing the modular multiplicative inverse. Hence, formula 71 is a reflexive generalized inverse of formula 69. The Jacobian also occurs in the inverse function theorem. This is also useful in deriving other inverse trigonometric forms below. The multiplicative inverse of only exists if and are coprime. There are several notations used for the inverse trigonometric functions. The reverse is possible by contracting with the (matrix) inverse of the metric tensor. Here formula 150 is the generalized inverse of formula 151. Random samples can be generated using inverse transform sampling. An approach to inverse uncertainty quantification is the modular Bayesian approach. There is a symmetry between a function and its inverse. Humanoid movement is calculated through unity inverse kinematics. A function with a left inverse is necessarily injective.