论文标题
基于Viète的公式$π$的余弦和余弦函数的嵌套公式
Nested formulas for cosine and inverse cosine functions based on Viète's formula for $π$
论文作者
论文摘要
在本文中，我们为余弦和余弦函数开发了嵌套表示形式，这是Viète的$π$公式的概括。我们探索这些表示形式之间的自然反向关系，并开发数值算法来计算它们。在本文中，我们对各种测试用例进行数值计算，并证明这些嵌套公式对于复杂的参数和$ k $ th的分支有效。我们将提出的结果进一步扩展到双曲线余弦和对数函数，并使用其他三角身份，探索正弦和切线函数及其对逆。
In this article, we develop nested representations for cosine and inverse cosine functions, which is a generalization of Viète's formula for $π$. We explore a natural inverse relationship between these representations and develop numerical algorithms to compute them. Throughout this article, we perform numerical computation for various test cases, and demonstrate that these nested formulas are valid for complex arguments and a $k$th branch. We further extend the presented results to hyperbolic cosine and logarithm functions, and using additional trigonometric identities, we explore the sine and tangent functions and their inverses.
