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在高中《代数》上册(以下简称为《课本》)的第194-195页上,《课本》通过一个例题即例7(3)给出了如下的一个三角公式: asina+bcosa=a~2+b~2sin~(1/2)(a+) (1)(其中角所在象限由a,b的符号确定,角的值由tg=b/a确定)。这本是一个非常有用的公式,然而由于公式(1)中角所在的象限是由a,b的符号来确定的,那么在具体的题目中,角就有可能在任何一个象限,这在实际应用中就显得很不方便,并易出错(限于篇幅,本文对此不加论述,读者可参阅文[1],[2]。如将公式(1)改成下面的公式,则应用起来就十分方便了。即改进为:
On the 194-195 pages of the “Algebra” upper volume of the high school (hereinafter referred to as “textbook”), the “textbook” gives a trigonometric formula as follows: Example 7 (3): asina+bcosa=a~2 +b~2sin~(1/2)(a+) (1) (where the quadrant of the angle is determined by the sign of a,b, and the value of the angle is determined by tg=b/a). This is a very useful formula. However, because the quadrant of the formula in (1) is determined by the signs of a and b, then in a specific problem, the corners are likely to be in any quadrant, which is actually The application is inconvenient and error-prone (for reasons of space, this article does not discuss it. Readers can refer to [1], [2]. If you change Formula (1) to the following formula, then it will be applied. It is very convenient. That is to improve: