Showing papers on "Inverse trigonometric functions published in 1985"
TL;DR: In this paper, a formula for the displacement field of a triangular dislocation loop in an infinite isotropic linear elastic solid was developed, in coordinate-free form, since no special care need be taken in dealing with the branches of inverse trigonometric functions which appear in the ‘solid angle' contribution to the displacement fields.
Abstract: A formula is developed, in coordinate-free form, for the displacement field of a triangular dislocation loop in an infinite isotropic linear elastic solid. For purposes of numerical calculations, the present prescription may be more useful than one given previously by Hirth and Lothe (1982), since no special care need be taken in dealing with the branches of inverse trigonometric functions which appear in the ‘solid angle’ contribution to the displacement field. The method developed for computing the solid angle is also valid for a triangular loop in an an isotropic elastic solid.
52 citations
01 Jan 1985
TL;DR: In this article, the Fourier character of cosine series and sine series is generalized to complex trigonometric series and a notion of complex convex sequences is developed generalizing a result of Young [1] concerning the integrability of Cosine series.
Abstract: The classical criterion for the Fourier character of cosine series and sine series is generalized to complex trigonometric series. Our treatment unifies the ideas applied to cosine and sine series. A notion of complex convex sequences is developed generalizing a result of Young [1] concerning the integrability of cosine series.
9 citations
01 Jan 1985
TL;DR: In this paper, Ramanujan gives more proofs in this chapter than in most of the later chapters, and several of the formulas are very intriguing and evince the ingenuity and cleverness of the author.
Abstract: Chapter 2 is fairly elementary, but several of the formulas are very intriguing and evince Ramanujan’s ingenuity and cleverness. Ramanujan gives more proofs in this chapter than in most of the later chapters.
3 citations
Book•
01 Jan 1985
TL;DR: Inverse Trigonometric Functions and their derivatives have been studied in the context of Graph Sketching as mentioned in this paper, where the Sine and Cosine functions of a graph are represented by their derivatives.
Abstract: Coordinate Systems on a Line.Coordinate Systems in a Plane.Graphs of Equations.Straight Lines.Intersections of Graphs.Symmetry.Functions and Their Graphs.Limits.Special Limits.Continuity.The Slope of a Tangent Line.The Derivative.More on the Derivative.Maximum and Minimum Problems.The Chain Rule.Implicit Differentiation.The Mean-Value Theorem.The Sign of the Derivative.Rectilinear Motion.Instantaneous Velocity.Instantaneous Rate of Change.Related Rates.Approximation by Differentials.Newton's Method.Higher-Order Derivatives.Applications of the Second Derivative.Graph Sketching.More Maxiumum and Minimum Problems.Angle Measure.The Sine and Cosine Functions.Graphs and Derivatives of the Sine and Cosine Functions.The Tangent and Other Trigonometric Functions.Antiderivatives.The Definite Integral.The Fundamental Theorem of Calculus.Applications of Integration I: Area and Arc Length.Applications of Exponential Growth and Decay.Inverse Trigonometric Functions.L'Hopital's Rule.Exponential Growth and Decay.Inverse Trigonometric Functions.Integration by Parts.Trigonometric Integrands.Trigonometric Substitutions.Integration of Rational Functions: The Method of Partial Fractions.Answers to Supplementary Problems.
1 citations
Patent•
09 Aug 1985
TL;DR: In this article, an inverse trigonometric function arithmetic circuit which is capable of a high-speed operation with simple constitution, by using a means which copies an image after deciding a range of application within a cycle of the inverse trigonal function which is read out of a ROM, was presented.
Abstract: PURPOSE:To obtain an inverse trigonometric function arithmetic circuit which is capable of a high-speed operation with simple constitution, by using a means which copies an image after deciding a range of application within a cycle of the inverse trigonometric function which is read out of a ROM CONSTITUTION:An input signal has the positive polarity in the first 1/4 cycle of a sine function supplied to an input terminal 1 At the same time, the primary function of the input signal is also positive Therefore a primary derived function code discriminator 8 outputs a signal having the positive polarity This needs no correction at all to the output of a ROM3, and a selector 15 has no changeover The value outputted from the RAM3 to a point P2 of the input signal is given at a point P3 The polarity of the primary derived function is changed negative in the following 1/4-1/2 periods, and the ROM3 outputs the value of the point P3 In this case, however -pi is added to the P3 owing to the negative polarity and an image is copied to a point P4 While the point P4 is copied to a point P5 with changeover of the selector 15 Thus P5 shows the reversed sine value of the P1
1 citations
TL;DR: Inverse hyperbolic functions as areas were studied in this article, with a focus on the Inverse Hyperbolic Functions as Areas (IHFAs) as a function as an area.
Abstract: (1985). Inverse Hyperbolic Functions as Areas. The College Mathematics Journal: Vol. 16, No. 2, pp. 129-131.
1 citations
TL;DR: In this paper, a Taylor's series expansion of some inverse trigonometric functions is proposed to perform the cartesian to joint coordinates conversion in real-time for SCARA robots.