若干多角和三角函数公式——从高中三角函数说起

Some Formulas of Trigonometric Functions with Multi-Angles—Starting from Trigonometric Functions in Senior High School

本文通过数学归纳法等给出了若干多角和三角函数展开式,即多角和的正弦、余弦和正切函数展开式。基于此我们还给出了若干相应的公式,如对Machin公式的推广。总之,本文对于高中阶段三角函数的教学和认识有一定的辅助作用。

With the mathematical induction and other methods at hand, this paper presentes some expressions of trigonometric functions with multi-angles, i.e. expressions of the sine, cosine and tangent functions. Based on these, we also give some corresponding formulas, for instance, the generalized Machin formulae. Above all, this paper plays an auxiliary role in the teaching and understanding of trigonometric function in senior high school.