三角函数最值问题

目录

摘要................................................................................................................................................... I I ABSTRACT ......................................................................................................................................... I II 第一章绪论.. (4)

1.1 三角函数的起源与发展 (4)

1.2 三角函数的最值问题 (4)

第二章解决三角函数最值问题的方法技巧 (6)

2.1 利用三角函数的定义、性质与函数图像解决最值问题 (6)

2.2 利用转化（或化归）思想解决最值问题 (7)

2.3 利用换元法解决最值问题 (10)

2.4 利用数形结合解决最值问题 (14)

2.5 利用不等式解决最值问题 (15)

第三章三角函数最值的简单应用 (17)

3.1 在数列中的简单应用 (17)

3.2 在不等式中的简单应用 (18)

3.3 在几何中的简单应用 (19)

3.4 在复数中的简单应用 (20)

第四章结论 (22)

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三角函数最值问题的若干讨论

学生：指导教师：

摘要三角函数的最值问题是三角函数基础知识的综合应用，在近几年的高考试题中经常出现，成为高考中的一个命题热点，同时也是高中数学必修课中的几大容之一。解决三角函数的最值问题不仅会用到三角函数的基本定义、单调性、奇偶性、周期性、有界性和三角函数图像，而且还会用到三角函数的多种恒等变化。同时，在三角函数的最值问题中常常涉及到初等函数、不等式、方程、几何等方面问题；而且在解决一些不等式、数列等问题中也会用三角函数的最值来求解。由此看来，三角函数的最值问题具有一定的综合性和灵活性。

本文将从具体的是实例出发，介绍并分析求解三角函数最值问题的几种基本方法和几种比较典型的解题方法，找出一般的解题方法和技巧；在介绍三角函数最值在数列、不等式等题型中的简单应用。

关键字：三角函数；最值；方法；技巧；应用

TRIGONOMETRIC NUMBER OF DISCUSSIONS ON THE QUESTION OF THE MOST V ALUE

Student:teacher:

ABSTRACT Trigonometry problem is the most value of trigonometric function that the basic knowledge of comprehensive application, In recent years the high exams often appears in, become a hot spot in the university entrance exam proposition, also the high school mathematics required courses in one of several major contents. To solve the most value of trigonometric function, not only can use ask basic trigonometric definition, monotony, parity, the periodicity, the boundedness and trigonometric functions image, and will use trigonometry multiple identical changes. Meanwhile, in the most value problem trigonometric function often involves elementary function,, inequality equation, a few problems; how And in solving some problems such as sequence, inequality will also be by trigonometric function of most value to solve. Consequently, the most value problem trigonometric function has certain comprehensive and flexibility.

This paper will start from the concrete examples, is introduced and analyzed the most value problem solving trigonometric functions of several basic method and several comparatively typical problem solving method, and find out the general problem solving methods and skills; In the introduction of the most value in the sequence of trigonometric function and inequality in regearching into simple application.

Key words:trigonometric function, optimum value, method, technique, adhibition