余弦公式

We derive the addition formulas for sine and cosine from the arithmetic of complex numbers.

用复数算术推导了正弦，余弦的加法公式。

We derive the addition formulas for sine and co sine from the arithmetic of complex numbers.

用复数算术推导了正弦，余弦的加法公式。

Based on the wave equation of longitudinal vibration of variable cross-session rod, the frequency equation and parameter formula of cosine horn are educed, the cosine horn with same frequency and different area ratio is designed by using Matlab language.

根据变截面杆纵向振动的波动方程，推导了余弦形变幅杆的频率方程和重要参数的计算公式。

The main contribution of this thesis is that we propose a collaborative filtering recommendation algorithm based on double clustering. This approach first respectively clusters resources and users by the users rating on items, then makes a collaborative filtering recommendation based on the clustering result. The new algorithm can shorten on-line recommendation time. Then, we apply the classical formula of cosine correlation to double clustering algorithm, leaving out the standardization operation. In the end, we implement an educational resource recommender system according to the need of the actual project and the result is positive.

本文的主要意义在于，首先运用聚类技术对用户和资源分别进行聚类，然后利用聚类结果进行协同过滤推荐，由于聚类部分离线周期进行，大大缩短了在线的推荐时间；然后将经典的余弦相似性计算公式运用到双重聚类算法中，省去规范化处理操作，减少运算量；最后结合实际的需要，实现一个资源推荐系统。

In this paper we introduce the hyperbolic cosine function and construct the new hyperbolic cosine penalty function and algorithms, further more, we construct the new hyperbolic cosine multipier penalty function .

本文在传统形式的罚函数基础上引入双曲余弦函数做罚项，构造了新的对于一般约束优化问题的双曲余弦罚函数和求解迭代公式；进一步地，又提出了求解具有等式约束优化问题的双曲罚函数乘子法。

In this paper,the methods of distance geometry are used to explore the angles of a simplex ,and the second cosine law of a simplex in another form is obtained.

运用距离几何的研究方法，研究了和单形相关的角，给出了单形第二余弦定理的另一种形式，以此为基础得出了BartO¨s体积公式一种简洁的证法；探讨了单形的几个体积公式之间的联系，并推广了单形的一个体积公式。

This procedure is based on discrete cosine transform DCT-formula implemented procedures to help beginners understand the discrete cosine transform process.

详细说明：这个程序是根据离散余弦变换的公式实现的DCT变换程序，能够帮助初学者理解离散余弦变换的过程。

The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived.

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究，采用将矩形域函数表示为复高斯函数叠加的技巧，推导出了解析的传输公式，在特殊情况下，该公式简化为在无光阑情况下的传输公式。

The propagation of elegant cosh-squared-Gaussian beams has been investigated and the analytic solutions have been obtained by means of an angular spectrum technique in uniaxially anisotropic crystals.

基于光束在单轴晶体中传输的角谱理论，对复宗量双曲余弦平方-高斯光束在单轴各向异性晶体中的传输作了研究，得到了一般的解析传输公式，并用数值的方法讨论了晶体内源于复宗量双曲余弦平方-高斯光束的两偏振分量的传输特性，结果表明，在适当参数的条件下，两偏振分量在晶体中的传输波形结构基本保持不变。

To satisfy the requirements of fast producing,low cost manufacture and large thickness preforming in the field of non-resin winding cylinder composite,the equation of retracing cosine curve was deduced based on the section principle.

为使复合材料圆柱壳体预制件适应短周期快速生产、低成本、壳体厚壁成型的要求，基于缠绕区段划分原理推导出端部余弦折回曲线方程，并结合传统纺织理论，推导了余弦折回曲线模型下端部特征参数计算公式。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。