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形如y=Asin(ωx+φ)+b的三角函数,是高中数学的重点,更是高考的热点。此类函数因其名称和角的多变性显得不易把握,为了让同学们易于理解和应用,笔者以高考题为例,把此类题目按求自变量、函数值和图像变换分为三类,提供相应的求解策略,供同学们学习时参考。一、“三字”诀适用于求与三角函数自变量x有关的问题,如求三角函数的定义域、函数取得最值时相应x的集合、单调区间、对称中心和对称轴、解三角方程或不等式问题。具体操作如下:
The trigonometric function such as y=Asin(ωx+φ)+b is the focus of high school mathematics, and it is also a hot spot of college entrance examination. Such functions are difficult to grasp due to the variability of their names and angles. In order to make the students easy to understand and apply, the author takes the college entrance examination question as an example to classify such topics into three categories according to the independent variables, function values, and image transformations. Provide corresponding solution strategies for students to learn when referencing. First, the “three-character” is applicable to the problems related to the trigonometric x, such as the definition of the trigonometric function, the set of corresponding x when the function obtains the maximum value, the monotonic interval, the symmetry center, and the symmetry axis. Trigonometric equation or inequality problem. The specific operation is as follows: