The Derivative of the Sine and Cosine. A New Derivation Approach

Fourier Cosine and Sine Transform on fractal space

In this paper, we establish local fractional Fourier Cosine and Sine Transforms on fractal space, considered some properties of local fractional Cosine and Sine Transforms, show applications of local fractional Fourier Cosine and Sine transform to local fractional equations with local fractional derivative.

Some applications of the sine and cosine integrals

We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.

余弦与正弦的幂

Powers of Cosine and Sine

本文研究正弦与余弦幂之和的表示问题，通过域扩张的基给出其表达式。

Introductory Calculus from the Viewpoint of Non-Standard Analysis - Derivative of Sine and Cosine

This article exemplifies a novel approach to the teaching of introductory differential calculus using the modern notion of ``infinitesimal'' as opposed to the traditional approach using the notion of ``limit''. I illustrate the power of the new approach with a discussion of the derivatives of the sine and cosine functions.

Spline Based Series for Sine and Arbitrarily Accurate Bounds for Sine, Cosine and Sine Integral

Based on two point spline approximations of arbitrary order, a series of functions that define lower bounds for sin(x) and sin(x)/x, over the interval [0,Pi/2], with increasingly low relative errors and smaller relative errors than published results, are defined. Second, fourth and eighth order approximations have, respectively, maximum relative errors over the interval [0,Pi/2] of 3.31 x 10-4, 2.48 x 10-8, and 2.02 x 10-18. New series for the sine function, which have significantly better convergence that a Taylor series over the interval [0,Pi/2], are proposed. Applications include functions…

On the derivatives of the powers of trigonometric and hyperbolic sine and cosine

This work contains different expressions for the k'th derivative of the n'th power of the trigonometric and hyperbolic sine and cosine. The first set of expressions follow from the complex definitions of the trigonometric and hyperbolic sine and cosine, and the binomial theorem. The other expressions are polynomial-based. They are perhaps less obvious, and use only polynomials in sin(x) and cos(x), or in sinh(x) and cosh(x). No sines or cosines of arguments other than x appear in these polynomial-based expressions. The final expressions are dependent only on sin(x), cos(x), sinh(x), or cosh(x)…