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本文将用初等数学的方法研究函数y=(c+bsinx)/(d+acosx)的极值问题:一、在什么条件下,函数y有极值;二、若函数有极值。那么怎样求极值。我们首先通过具体例题来研究如果函数有极值的情况下,怎样求极值例1 求函数y=(1-3sinx)/(5+2cosx)的极值。解法一:去分母整理得: 3sinx+2ycosx=1—5y, ■(9+4y~2)~(1/2)sin(x+φ)=1-5y,φ=arctg(2y)/3, ■sin(x+φ)=(1-5y)/(9+4y~2)~(1/2)
This paper will use elementary mathematics to study the extremum of the function y=(c+bsinx)/(d+acosx): First, under what conditions, the function y has extreme values; Second, if the function has extreme values. So how to find extremum. We first study how to find the extremum if the function has an extremum through a concrete example. Find the extremum of the function y=(1-3sinx)/(5+2cosx). Solution one: Finishing to the denominator: 3sinx+2ycosx=1-5y, ■(9+4y~2)~(1/2)sin(x+φ)=1-5y, φ=arctg(2y)/3, ■sin(x+φ)=(1-5y)/(9+4y~2)~(1/2)