Relevant bibliographies by topics / Inverse trigonometric functions

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Inverse trigonometric functions'

Author: Grafiati
Published: 7 September 2021
Last updated: 1 February 2022

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Journal articles on the topic "Inverse trigonometric functions"

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Barrera, Azael. "Unit Circles and Inverse Trigonometric Functions." Mathematics Teacher 108, no. 2 (September 2014): 114–19. http://dx.doi.org/10.5951/mathteacher.108.2.0114.

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Mesa, Vilma, and Bradley Goldstein. "Conceptions of Angles, Trigonometric Functions, and Inverse Trigonometric Functions in College Textbooks." International Journal of Research in Undergraduate Mathematics Education 3, no. 2 (October 20, 2016): 338–54. http://dx.doi.org/10.1007/s40753-016-0042-1.

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Wallace, Edward C. "Investigations Involving Involutions." Mathematics Teacher 81, no. 7 (October 1988): 578–79. http://dx.doi.org/10.5951/mt.81.7.0578.

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Many second-year algebra textbooks include a discussion of functions and their inverses prior to introducing logarithms and the inverse trigonometric functions. Since these functions and some others can be approached neatly as inverses of more familiar functions, a good understanding of the notion of inverse allows students to understand these topics better.
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Neel, Matthew. "Transcendental Functions and Tangent Circles." Mathematics Teacher 112, no. 1 (September 2018): 71–74. http://dx.doi.org/10.5951/mathteacher.112.1.0071.

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These are functions that are not algebraic. The set of transcendental functions includes the trigonometric, inverse trigonometric, exponential and logarithmic functions, but it also includes a vast number of other functions that have never been named…. (Stewart 1999, p. 35)
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Chen, Chao-Ping, and József Sándor. "Inequality chains related to trigonometric and hyperbolic functions and inverse trigonometric and hyperbolic functions." Journal of Mathematical Inequalities, no. 4 (2013): 569–75. http://dx.doi.org/10.7153/jmi-07-53.

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Aprahamian, Mary, and Nicholas J. Higham. "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms." SIAM Journal on Matrix Analysis and Applications 37, no. 4 (January 2016): 1453–77. http://dx.doi.org/10.1137/16m1057577.

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Li, Bo, Yan Zhang, and Xiquan Liang. "Several Differentiation Formulas of Special Functions. Part III." Formalized Mathematics 14, no. 1 (January 1, 2006): 37–45. http://dx.doi.org/10.2478/v10037-006-0006-z.

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Several Differentiation Formulas of Special Functions. Part III In this article, we give several differentiation formulas of special and composite functions including trigonometric function, inverse trigonometric function, polynomial function and logarithmic function.
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Zhang, Bo, and Chao-Ping Chen. "Sharp Wilker and Huygens type inequalities for trigonometric and inverse trigonometric functions." Journal of Mathematical Inequalities, no. 3 (2020): 673–84. http://dx.doi.org/10.7153/jmi-2020-14-43.

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Wells, Cacey. "Exploring Accessibility: An Application of Inverse Trigonometric Functions." Mathematics Teacher 112, no. 6 (April 2019): 480. http://dx.doi.org/10.5951/mathteacher.112.6.0480.

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Each school year, students enter our classrooms with unique experiences and perspectives that ought to be shared. One year, I noticed a student in our school who used a wheelchair. When I saw how difficult it was for that student to navigate the ramps in our school, I began to think about a trigonometry lesson focused on accessibility. I wanted to use mathematics to explore what life was like—albeit to a minor degree—for those with disabilities. The lesson objective was to explore angles of incline in wheelchair ramps to determine whether such ramps truly offer accessibility.
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Baricz, Árpád, Ali Bhayo, and Matti Vuorinen. "Turán type inequalities for generalized inverse trigonometric functions." Filomat 29, no. 2 (2015): 303–13. http://dx.doi.org/10.2298/fil1502303b.

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In this paper we study the inverse of the eigenfunction sinp of the one-dimensional p-Laplace operator and its dependence on the parameter p, and we present a Tur?n type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur?n type inequality for a series considered by Ramanujan, involving the digamma function.
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Dissertations / Theses on the topic "Inverse trigonometric functions"

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Dias, Maria de Fátima Castilho. "Uma abordagem para análise, classificação e resolução de problemas que envolvem trigonometria : exemplos de aplicação." Master's thesis, Universidade de Évora, 2010. http://hdl.handle.net/10174/20921.

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Como professora de matemática, com experiência no Ensino Secundário, tenho constatado que os alunos revelam bastantes dificuldades de compreensão, aquisição e aplicação dos conteúdos trigonométricos. Também os conteúdos de trigonometria dos actuais manuais escolares do ensino secundário não são suficientes para aqueles alunos que pretendem seguir estudos superiores nas áreas da Física, da Matemática, da Engenharia, Este trabalho destina-se essencialmente a esse grupo de alunos, mas também pode servir de material de apoio a professores do Ensino Básico/Secundário que queiram enriquecer e aprofundar os seus conhecimentos nesta área. Ao longo deste trabalho, propomos uma forma alternativa de apresentação deste tema, pensamos que deste modo os alunos possam compreender "como, donde e porquê" aparecem as relações trigonométricas. Classificamos e analisamos em profundidade equações trigonométricas, com a finalidade de propor abordagens diferentes de resolução, umas típicas outras originais. Analisamos desigualdades trigonométricas e sistemas de equações trigonométricas utilizando métodos de resolução distintos. Apresentamos versões distintas de demonstrações para as mesmas afirmações, e apresentamos problemas de Geometria, de Topografia e de Física, mostrando desta forma a aplicação prática da Trigonometria. Finalizamos este trabalho com a apresentação de algumas relações trigonométricas na teoria dos Números Complexos. – ABSTRACT: School students, I have noticed that students have many difficulties in understanding trigonometric contents. The contents related to trigonometry that are presented, in modem textbooks adopted by Secondary Schools are not enough for those students who intend to take a degree in areas in field of physics, mathematics and engineering. This study is essentially intended for the above-mentioned students, but it can also be used as a support material for a secondary school teachers who want to enrich and increase their scientific knowledge in the field of trigonometry. This project suggests an alternative way to introduce the topic so that student can understand "how, from, where and why" trigonometric relationships appear. Trigonometric equations are classified and examined deeply in order to suggest different approaches for their solution, typical ones and original others. Trigonometric inequalities and systems of trigonometric equations of special types are also analysed using different solution methods. Different versions of demonstrations for the same statements are presented as well as problems of Geometry, Topography and Physics, with the purpose of showing the practical use of trigonometry. This project ends with the presentation of some trigonometric relationships in the theory of Complex Numbers.
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Book chapters on the topic "Inverse trigonometric functions"

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Vilhelm, Václav. "Trigonometric and Inverse Trigonometric Functions. Hyperbolic and Inverse Hyperbolic Functions." In Survey of Applicable Mathematics, 69–94. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8308-4_2.

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Rahmani-Andebili, Mehdi. "Problems: Trigonometric and Inverse Trigonometric Functions." In Precalculus, 83–87. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65056-8_11.

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Gelfand, I. M., and Mark Saul. "Inverse Functions and Trigonometric Equations." In Trigonometry, 207–29. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0149-6_10.

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Morais, João Pedro, Svetlin Georgiev, and Wolfgang Sprößig. "Inverse Hyperbolic and Trigonometric Functions." In Real Quaternionic Calculus Handbook, 125–32. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0622-0_8.

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Rahmani-Andebili, Mehdi. "Solutions of Problems: Trigonometric and Inverse Trigonometric Functions." In Precalculus, 89–100. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65056-8_12.

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Bird, John. "Differentiation of inverse trigonometric and hyperbolic functions." In Bird's Higher Engineering Mathematics, 386–96. 9th ed. Ninth edition. | Abingdon, Oxon ; New York : Routledge, 2021.: Routledge, 2021. http://dx.doi.org/10.1201/9781003124221-31.

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Lester, David. "Using PVS to Validate the Inverse Trigonometric Functions of an Exact Arithmetic." In Numerical Software with Result Verification, 259–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24738-8_16.

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Lower, Michał. "High Quality Stabilization of an Inverted Pendulum Using the Controller Based on Trigonometric Function." In Advances in Dependability Engineering of Complex Systems, 244–53. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59415-6_24.

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"Inverse Trigonometric Functions and Trigonometric Equations." In Trigonometric Functions and Complex Numbers, 97–119. WORLD CENTURY PUBLISHING CORPORATION, 2016. http://dx.doi.org/10.1142/9781938134876_0004.

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JOHNSON, R. M. "Inverse Trigonometric and Hyperbolic Functions." In Calculus, 202–18. Elsevier, 1995. http://dx.doi.org/10.1533/9780857099860.202.

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Conference papers on the topic "Inverse trigonometric functions"

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Michopoulos, John G., and Athanasios Iliopoulos. "High Dimensional Full Inverse Characterization of Fractal Volumes." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71050.

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The present paper describes a methodology for the inverse identification of the complete set of parameters associated with the Weirstrass-Mandelbrot (W-M) function that can describe any fractal scalar field distribution of measured data defined within a volume. Our effort is motivated by the need to be able to describe a scalar field quantity distribution in a volume in order to be able to represent analytically various non-homogeneous material properties distributions for engineering and science applications. Our method involves utilizing a refactoring of the W-M function that permits defining the characterization problem as a high dimensional singular value decomposition problem for the determination of the so-called phases of the function. Coupled with this process is a second level exhaustive search that enables the determination of the density of the frequencies involved in defining the trigonometric functions involved in the definition of the W-M function. Numerical applications of the proposed method on both synthetic and actual volume data, validate the efficiency and the accuracy of the proposed approach. This approach constitutes a radical departure from the traditional fractal dimension characterization studies and opens the road for a very large number of applications and generalizes the approach developed by the authors for fractal surfaces to that of fractal volumes.
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Michopoulos, John G., and Athanasios Iliopoulos. "Complete High Dimensional Inverse Characterization of Fractal Surfaces." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47784.

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The present paper describes a methodology for the inverse identification of the complete set of parameters associated with the Weirstrass-Mandelbrot (W-M) function that can describe any rough surface known by its profilometric or topographic data. Our effort is motivated by the need to determine the mechanical, electrical and thermal properties of contact surfaces between deformable materials that conduct electricity and heat and require an analytical representation of the surfaces involved. Our method involves utilizing a refactoring of the W-M function that permits defining the characterization problem as a high dimensional singular value decomposition problem for the determination of the so-called phases of the function. Coupled with this process is a second level exhaustive search that enables the determination of the density of the frequencies involved in defining the trigonometric functions involved in the definition of the W-M function. Our approach proves that this is the only additional parameter that needs to be determined for full characterization of the W-M function as the rest can be selected arbitrarily. Numerical applications of the proposed method on both synthetic and actual elevation data, validate the efficiency and the accuracy of the proposed approach. This approach constitutes a radical departure from the traditional fractal dimension characterization studies and opens the road for a very large number of applications.
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Carricato, Marco, Joseph Duffy, and Vincenzo Parenti-Castelli. "Inverse Static Analysis of a Planar System With Spiral Springs." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/mech-14199.

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Abstract In this article the inverse static analysis of a two degrees of freedom planar mechanism equipped with spiral springs is presented. Such analysis aims to detect the entire set of equilibrium configurations of the mechanism once the external load is assigned. While on the one hand the presence of flexural pivots represents a novelty, on the other it extremely complicates the problem, since it brings the two state variables in the solving equations to appear as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to write two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention has been reserved to the analysis of the “reliability” of the final equations: it has been sought the existence of critical situations, in which the solving equations hide solutions or yield false ones. A numerical example is provided. Also, in Appendix it is shown a particular design of the mechanism that offers computational advantages.
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Arikawa, Keisuke. "Symbolic Computation of Inverse Kinematics for General 6R Manipulators Based on Raghavan and Roth’s Solution." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22231.

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Abstract We discuss the symbolic computation of inverse kinematics for serial 6R manipulators with arbitrary geometries (general 6R manipulators) based on Raghavan and Roth’s solution. The elements of the matrices required in the solution were symbolically calculated. In the symbolic computation, an algorithm for simplifying polynomials upon considering the symbolic constraints (constraints of the trigonometric functions and those of the rotation matrix), a method for symbolic elimination of the joint variables, and an efficient computation of the rational polynomials are presented. The elements of the matrix whose determinant produces a 16th-order single variable polynomial (characteristic polynomial) were symbolically calculated by using structural parameters (parameters that define the geometry of the manipulator) and hand configuration parameters (parameters that define the hand configuration). The symbolic determinant of the matrix consists of huge number of terms even when each element is replaced by a single symbol. Instead of expressing the coefficients in a characteristic polynomial by structural parameters and hand configuration parameters, we substituted appropriate rational numbers that strictly satisfy the constraints of the symbols for the elements of the matrix and calculated the determinant (numerical error free calculation). By numerically calculating the real roots of the rational characteristic polynomial and the joint angles for each root, we verified the formulation for the symbolic computation.
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Moore, B., and E. Oztop. "Redundancy Parameterization for Flexible Motion Control." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28387.

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Our overall research interest is in synthesizing human like reaching and grasping using anthropomorphic robot hand-arm systems, as well as understanding the principles underlying human control of these actions. When one needs to define the control and task requirements in the Cartesian space, the problem of inverse kinematics needs to be solved. For non-redundant manipulators, a desired end-effector position and orientation can be achieved by a finite number of solutions. For redundant manipulators however, there are in general infinitely many solutions where the cardinality of the solution set must be made finite by imposing certain constraints. In this paper, we consider the Mitsubishi PA10 manipulator which is similar to the human arm, in the sense that both wrist and shoulder joints can be considered to emulate a 3DOF ball joint. We explicitly derive the analytic solution for the inverse kinematics using quaternions. Then, we derive a parameterization in terms of a pure quaternion called the swivel quaternion. The swivel quaternion is similar to the elbow swivel angle used in most approaches, but avoid the computation of inverse trigonometric functions. This parameterization of the self-motion manifold is continuous with any end-effector motion. Given the pose of the end-effector and the swivel quaternion (or swivel angle), the algorithm derives all solution of the inverse kinematics (finite number). We then show how the parameterization of the elbow self-motion can be used for the real-time control of the PA10 manipulator in the presence of obstacles.
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