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.

Hardware implementation of coordinate rotation digital computer in field programmable gate array

Abstract: Trigonometry is of great importance in mathematics as well as in physics, engineering, and chemistry. Astronomy, geography, navigation, study of optics and acoustics, oceanography, architecture, calculus, etc. are just several examples where trigonometry is significantly practiced. Historical figures like Pythagoras and Columbus used trigonometric tables in their careers. The birth of software has empowered relatively faster trigonometric functions performed by processors. In real-time applications though, such as trajectory calculations in military or space exploration, or in biomedical authentication system for fast access or rejection decision, trigonometric computation by software is a considerably time-consuming process. Coordinate Rotation Digital Computer (CORDIC) is an algorithm developed for hardware implementation as a real-time solution to trigonometric computation. This report presents a design approach to realize the CORDIC algorithm, prototyped as an embedded system in an Altera Field Programmable Gate Array (FPGA) development board running at 100 MHz clock frequency. The design flow applies the systematic Register Transfer Level (RTL) methodology, partitioning the design into a Datapath Unit (DU) for computation tasks, and a Control Unit (CU) for controlling the operation flow. Experimental results show that a high accuracy was obtained, with mean computation errors between 0.0014% and 0.0023% with respect to a software implementation on the same platform. The speed up in the execution time is about 89 times for the computation of cosine and sine functions, and 69 times for the arctangent. The work demonstrates the power of the CORDIC algorithm, and presents a methodology for an efficient complex hardware design.

Some comments on inverse arithmetic functions

Abstract: In many of the basic courses in Number Theory, Finite Mathematics and Cryptography we come across the so-called arithmetic functions such as ϕn), σ(n), τ(n), μ(n), etc, whose domain is the set of natural numbers. These functions are well known and evaluated through the prime factor decomposition of n. It is less well known that these functions possess inverses (with respect to Dirichlet multiplication) which have interesting properties and applications.

Mathematics Solutions for Inverse Tangents

Abstract: Sinusoidal circuit analysis is very co mmon in Alternating Current (AC) electrical circu it analysis and so close to the term of phasor concept using complex frequency, which is mainly use trigonometry figures such as sin, cos, and tangent, for calculations. One of the most important tasks that we will meet e.g. finding phase angles using inverse tangent formu la. The author presents this paper to introduce a mathematic solution derived fro m basic concept of trigonometry, to solve circuit analysis problems related to phase angles and inverse tangents.

A Generalization of the Angle Doubling Formulas for Trigonometric Functions

Abstract: SummaryThe angle doubling formula sin 2θ = 2 sin θ cos θ for the sine function is well known. By replacing the cosine in this formula with sin (π/2 - θ), we see that sin 2θ can be written as the product of two sine functions where the second sine function is obtained from the basic sine function by only using a phase shift of the angle θ and a reflection about the horizontal axis. In this paper, we will show that, for any natural number n, sin nθ can be written as the product of n sine functions involving only phase shifts of the angle θ and a possible reflection about the horizontal axis. Similar formulas will be derived for the cosine and tangent functions.