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三角函数通常定义为包含这个角的直角三角形的两个边的比率,也可以等价地定义为单位圆上的各种线段的长度。更现代的定义是把它们表达为无穷级数或特定微分方程的解,允许它们扩展到任意正数和负数值,甚至是复数值。前人已找到了无数的三角函数公式:倍角公式、半角公式、和差化积、积化和差公式、双曲函数……其中一些公式的证明较复杂,本文从微分角度,运用几何方法证明三角函数极限公式
The trigonometric function is usually defined as the ratio of the two sides of a right-angled triangle that contains this corner. It can also be equivalently defined as the length of various line segments on a unit circle. A more modern definition is to express them as solutions to an infinite series or a particular differential equation, allowing them to be extended to any positive and negative or even complex values. The predecessors have found countless trigonometric functions: multiplier, half-angle, differential product, product of sum and difference, hyperbolic function ... Some of the formulas prove more complicated. This paper uses the geometric method to prove Trigonometric function limit formula