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设置参数(即参变量),将问题转化,是解决数学问题的一个重要策略。许多较难的数学问题,若能选择恰当的中间参变量,将问题转化,从而创造条件,以便使用熟悉的定理或公式,降低解题难度,摆脱冗繁的运算,对启迪思维,开发智力,提高能力,培养对数学的兴趣,都能起到良好的作用。现以三角题为例,说明设参转化,简捷求解的方法与技巧,供同学们参考。一、整体设参例1 化简(?),其中α为第二象限角。简析设原式=t, 则(?) α为第二象限角,∴t=-2tanα。
Setting parameters (that is, parameter variables) to transform problems is an important strategy for solving math problems. Many difficult math problems, if you can choose the right middle parameter, transform the problem, and create conditions to use familiar theorems or formulas to reduce the difficulty of solving problems, get rid of tedious operations, to inspire thinking, develop intelligence, improve Ability to cultivate interest in mathematics can all play a good role. Taking the trigonometry problem as an example, the methods and techniques for the transformation of setting parameters and simple solutions are explained for students’ reference. First, the overall design of the reference example 1 simplify (?), where α is the second quadrant angle. Simple analysis of the original formula = t, then (?) α is the second quadrant angle, ∴t = -2tanα.