摘要: 如果一个函数在一点的一个邻域内处处都有确定的值，而以该点处的值为最大（最小），这函数在该点处的值就是一个极大（极小）值。极值问题难点在于要确定它在哪些点处达到最大值或最小值.如果不是有界闭区间的边界点就一定是内点.极值问题在日常生活中经常遇到，不管是自然科学、工程技术，还是生产活动、生活实践中都有极值问题的存在,类型也是多种多样的,其中复合三角函数的极值却占着重要的地位,因为它不但能解决三角函数的极值问题,而且许多其它类型的函数极值问题通过变换往往可化为这一类型. 现行全日制普通高级中学教材中, 有关三角函数式极值问题的例题和解法却甚少,本文仅就三角函数极值问题进行讨论，并根据不同类型的函数式，利用不同的方法归纳成解决此类问题的五种常用的方法，供中学教师教学中参考。

关键字：三角函数;极值；解法

Abstract: If a function in a neighborhood of a point in all determined values,and to the point value for the maximum (minimum), this function is a maximum（minimum）at the point of the value. Extremum problem is difficult to determine which it reaches the maximum or minimum value at which point. If it is not bounded closed interval boundary points must be interior point extremal problem often encountered in daily life, whether it is natural science, engineering technology, or the production of extremum problems, all activities in the practice of life existence, the type is various, including extreme composite trigonometric function has occupied an important position, because it can not only solve the extremum problem of trigonometric function extremum problems, and many other types of the transform can often be of this type . The current senior high school textbooks, the formula of trigonometric function extremum problems. And the solution is little, this paper just as the trigonometric function extremum problem is discussed, and according to the function of various types, classified into five kinds of methods to solve these problems using different methods, for the reference of middle school teachers in teaching.

Key words: trigonometric function; extremum; solution