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式子asinα+bcosα=(a~2+b~2)~(1/2)sin(α+φ)(其中φ角所在的象限由a、b的符号确定,φ角的值由tgφ=b/a确定)在现行高中课本《代数》(甲种本)第一册P206页上已给出,但此后对它的应用没有涉及。因此,学生对这个公式的作用认识不足、体会不深。实际上该式在三角变换中是一个很有用的公式,如能在解题时灵活地应用它,能使方法简捷。本文就该式在解题中的应用简述如下,供参考。 1、求值例1 若sinx+cosx=1, 求sin~nx+cos~nx的值。
The formula asinα+bcosα=(a~2+b~2)~(1/2)sin(α+φ) (where the quadrant of the φ angle is determined by the signs of a and b, and the value of the φ angle is tgφ=b /a OK) is given on the P206 page of the current high school textbook Algebra (Type A), but it has not been applied to it since then. Therefore, the students’ understanding of the function of this formula is insufficient and the experience is not deep. In fact, this formula is a very useful formula in the trigonometric transformation. If you can apply it flexibly when solving a problem, it can make the method simple. This article briefly describes the application of the formula in solving problems as follows. 1. Evaluation Example 1 If sinx+cosx=1, find the value of sin~nx+cos~nx.