共查询到20条相似文献,搜索用时 62 毫秒
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有关三角函数的单调区间的确定或比较三角函数值的大小等问题,一般先将函数化成基本三角函数的形式,借助于单位圆或三角函数的图像来处理,数形结合思想是处理三角函数有关问题的重要方法. 相似文献
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三角函数是基本初等函数之一,也是数学竞赛的热点内容.三角函数具有一系列优美的性质,竞赛中涉及的考点主要有:三角函数的定义域、值域和有界性,三角函数的奇偶性、单调性、周期性、对称性,三角函数的图象的变换,三角恒等变换与三角不等式,与三角函数有关的最值问题,等等. 相似文献
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一、中考内容要求1.了解锐角的三角函数,知道30°,45°,60°的三角函数值;2.会用计算器求锐角的三角函数,已知三角函数求锐角;3.运用三角函数解决与直角三角形有关的简单实际问题.二、考法分析 相似文献
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笔者分析高中三角函数的课程内容、学业质量要求和近年高考中的三角函数的考查视角、分值等,查阅国内关于三角函数学习、教学的文献,梳理分析当前关于高中三角函数学习与教学的研究成果,探讨指向高中数学学科核心素养的三角函数教学的新的实践研究空间. 相似文献
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三角函数是基本初等函数之一,也是数学竞赛的热点内容.三角函数具有一系列优美的性质,竞赛中涉及的考点主要有:三角函数的定义域、值域和有界性,三角函数的奇偶性、单调性、周期性、对称性,三角函数的图象的变换,三角恒等变换与 相似文献
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三角函数线是三角函数的几何形式,高中数学课本应用三角函数线作出了正弦函数的图像.本文再介绍三角函数线在求角、求值、解证三角不等式、反三角函数等方面的应用.巧用三角函数线解题直观、简便. 相似文献
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高中数学三角函数公式比较多,而高考中涉及三角函数的计算、化简、证明等问题又都是对公式的考查.因此,学好三角函数,必须要掌握好三角函数公式的应用,而要真正掌握三角函数公式的应用,就要把握好下面三重层次,做到逐层递进,螺旋上升. 相似文献
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Yuanpeng Zhu & Xuli Han 《计算数学(英文版)》2015,33(6):642-684
Four new trigonometric Bernstein-like basis functions with two exponential shape parameters are constructed, based on which a class of trigonometric Bézier-like curves, analogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an ellipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cubic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape parameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be $C^2$ ∩ $FC^3$ continuous for a non-uniform knot vector, and $C^3$ or $C^5$ continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for $G^1$ continuous joining two trigonometric Bézier-like patches over triangular domain are deduced. 相似文献
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The aim of this study is to examine prospective mathematics teachers’ generalizations of trigonometric functions from the unit circle to the Cartesian coordinate system. The researcher developed a test that aimed to reveal students’ generalizations, as well as the possible differences between them. The test was administered to 30 students who were near completion of their university degree program. The findings showed that the students were unable to establish the link between the unit circle and the Cartesian coordinate representation system; and therefore, they were not able to interpret the outputs of trigonometric functions with input of a real number that is not a multiple of π. The researcher also found that the students had developed certain misconceptions regarding the properties of trigonometric functions. To improve the teaching of trigonometric functions an instructional sequence and an alternative definition for trigonometric functions is proposed. 相似文献
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We discuss error representations for Hermite-Lagrange trigonometric interpolation introduced in Dryanov and Petrov (Interpolation and L 1-approximation by trigonometric polynomials and blending functions, J. Approx. Theory 164, 1049–1064 (2012)) and obtain one-sided trigonometric quadratures for approximate integration of one-dimensional integrals. Next, we study error representations of multivariate Hermite-Lagrange transfinite trigonometric interpolation and derive one-sided trigonometric blending interpolants to multivariate functions, under some restrictions. Then, we construct one-sided transfinite cubature formulae for approximate integration of multivariate integrals. We construct also cubature formulae with positive coefficients, based on line integrals and exact in a vector space of trigonometric blending functions with prescribed order. 相似文献
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Using generating trigonometric functions, Bessel functions ofthe zero and first orders are expressed in terms of infiniteseries of trigonometric functions. The expansions are exactand in a truncated form may be used for accurate and rapid computationof the above or higher order Bessel Functions. 相似文献
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A new quadrature formula implemented on a nonstandard basis of trigonometric functions is constructed. The quadrature is comparable in accuracy to a Gaussian quadrature formula and is used with the same class of functions. However, this quadrature differs greatly from that for periodic functions, which is also based on trigonometric functions. 相似文献
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V. I. Arnold 《Functional Analysis and Its Applications》2002,36(3):165-171
Upper bounds for ergodic averages of topological characteristics of pseudoperiodic functions and manifolds are found in terms of the degrees of trigonometric polynomials defining these functions and manifolds. The bounds are based on finding the longest trigonometric and spherical curves of a fixed degree. 相似文献
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By using the Hirota’s bilinear method, the bilinear form of the sixth-order Ramani equation is succinctly obtained. With the aid of the obtained bilinear form, some new interaction solutions which include interaction solutions between exponential and trigonometric functions, interaction solutions between exponential and hyperbolic functions, and interaction solutions between trigonometric and hyperbolic functions are also presented by employing the three wave method. 相似文献
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运用复分析方法,首次给出了一类由三角函数、指数函数与幂函数乘积的线性组合产生的函数在某个区间上恒为零的充分必要条件证明,建立了此类函数积分计算的理论基础,结合微分和线性代数思想,系统讨论了待定系数法在一类含有三角函数的积分计算中的应用. 相似文献
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E. S. Belinskii 《Transactions of the American Mathematical Society》1998,350(1):43-53
The main problem considered in this paper is the approximation of a trigonometric polynomial by a trigonometric polynomial with a prescribed number of harmonics. The method proposed here gives an opportunity to consider approximation in different spaces, among them the space of continuous functions, the space of functions with uniformly convergent Fourier series, and the space of continuous analytic functions. Applications are given to approximation of the Sobolev classes by trigonometric polynomials with prescribed number of harmonics, and to the widths of the Sobolev classes. This work supplements investigations by Maiorov, Makovoz and the author where similar results were given in the integral metric.