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一、关于改进三角函数定义的一点设想 基本设想及其根据。三角函数是五种基本初等函数之一,它与幂函数、指数函数和对数函数比较起来,显得内容庞杂。这除了三角函数所研究的内容较多这一客观原因以外,三角函数的定义方法是人为的造成内容庞杂的一个主观原因。幂函数、指数函数和对数函数都只有一种形式（幂函数形如 y=x~n,指数函数形如 y=a~x,对数函数形如 y=log_ax）,而三角函数却有六种形式之多。据此,我们有理由设想,在不减少研讨内容的前提下,把三角函数也用一种形式定义出来。 在中学数学教材中,六种三角函数分别定义为sina=y/r（正弦函数)、cosa=x/r（余弦函数)、tga=y/x（正切函数）、ctga=x/y(余切函数)、seca=r/x(正割函数）和csca=r/y（余割函数）,其中p（x,y）是角a的终边上任意一点,r是P点到坐标原点的距离。
First, on the definition of trigonometric function to improve the basic idea of a little idea and its basis. Trigonometric functions are one of the five basic elementary functions that appear to be complex in comparison with power functions, exponential functions and logarithmic functions. Except for the objective reason that the trigonometric functions have more contents to study, the definition of trigonometric functions is a subjective reason for the man-made complex content. Power, exponential and logarithmic functions have only one form (power functions such as y = x ~ n, exponential functions like y = a ~ x and logarithmic functions like y = log_ax), while trigonometric functions have As many as six forms. Accordingly, we have reason to assume that the trigonometric functions are also defined in a form without reducing the scope of the study. In high school math textbooks, the six trigonometric functions are defined as sina = y / r (cosine function), cosa = x / r (cosine function), tga = y / Where seq = r / x (secant function) and csca = r / y (cosept function) where p (x, y) is any point on the end of the angle a, r is the point P to the coordinate origin distance.