Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
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TL;DR: In this article, the principal inverse tangent and cotangent functions for complex arguments are modified in such a way that they become odd on the imaginary axis, by choosing the other branch on the lower branch cut, and corresponding addition formulas for complex and real arguments are derived.
Abstract: The principal inverse tangent and cotangent functions for complex arguments can be defined as formulas involving principal natural logarithms, but these are not odd on the imaginary axis, which they must be according to their definitions as inverse functions. These formulas are therefore modified in such a way that they become odd on the imaginary axis, by choosing the other branch on the lower branch cut, and the corresponding addition formulas for complex and real arguments are derived. With these addition formulas their values on their branch cuts are determined, confirming these modified formulas. Some new formulas for the (hyperbolic) inverse tangent and cotangent functions for complex arguments and some new addition formulas for these functions for real arguments are derived. Some new formulas for the inverse sine and cosine functions and their connections with the inverse tangent and cotangent functions for complex arguments are provided, and from these some new addition formulas for the inverse sine and cosine functions for real arguments are derived. Some duplication and bisection formulas for the inverse tangent, cotangent, sine and cosine functions are derived.
01 Jul 2013
TL;DR: CORDIC based architecture is proposed to evaluate the trigonometric or inverse trigonometry functions like sinθ, cosθ to evaluate Finger print recognition process.
Abstract: Finger print recognition process involves many trigonometric evolutions. CORDIC based evolution of trigonometric functions is possible. In this paper CORDIC based architecture is proposed to evaluate the trigonometric or inverse trigonometric functions like sinθ, cosθ. Proposed architecture is partitioned into two main blocks: Magnitude generator and CORDIC processor. Magnitude generator outputs the value of the trigonometric function by driving the CORDIC processor. CORDIC processor executes the CORDIC rotations. Architecture Proposed in this paper is implemented using XILINX 13.2. Performance of the architecture is analyzed by calculating the relative error and resource utilization summery is reported.
01 Jan 2004
TL;DR: Trigonometric functions appear very frequently in mechanism kinematic equations (for example as soon a revolute joint is involved in the mechanism) and trigonometric substi- tutions are used to transform them into algebraic terms that can be handled more easily as mentioned in this paper.
Abstract: Trigonometric functions appear very frequently in mechanism kinematic equations (for example as soon a revolute joint is involved in the mechanism). Dealing with these functions is di cult and trigonometric substi- tutions are used to transform them into algebraic terms that can be handled more easily. We present briefly the origin of the trigonometric functions and of these substitutions.