求函数f(x)=5根号3cos^2x+根号3sin^2x-4sinxcox(兀/4≦x≦7兀/24)的最小值,并求其取得最小值时x的值.(函数要化成sin的形式)
求函数f(x)=5根号3cos^2x+根号3sin^2x-4sinxcox(兀/4≦x≦7兀/24)的最小值,并求其取得最小值时x的值.(函数要化成sin的形式)
其他人气:966 ℃时间:2019-11-22 00:12:40
优质解答
(sqrt是开方)f(x) = 5sqrt(3) [cos(2x)]^2 + sqrt(3) [sin(2x)]^2 - 4sin(x)cos(x),由于 [cos(2x)]^2 + [sin(2x)]^2 = 1,且 2sin(x)cos(x) = sin(2x),故= 5sqrt(3) {1-[sin(2x)]^2} + sqrt(3) [sin(2x)]^2 - 2sin(2x...
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