(cosx+sinx)平方+根号3倍cos2x-1在区间(O,π/2)的最大值和最小值

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 16:58:27

(cosx+sinx)平方+根号3倍cos2x-1在区间(O,π/2)的最大值和最小值
(cosx+sinx)平方+根号3倍cos2x-1在区间(O,π/2)的最大值和最小值

(cosx+sinx)平方+根号3倍cos2x-1在区间(O,π/2)的最大值和最小值
y=(sinx+cosx)²+√3cos2x-1
=sin²x+cos²x+2sinxconx+√3cos2x-1
=1+sin2x+√3cos2x-1
=2sin(2x+π/3)
0

(cosx+sinx)平方+根号3倍cos2x-1
=cos²x+sin²x+sin2x+√3cos2x-1
=sin2x+√3cos2x
=2sin(2x+π/3)
π/3<2x+π/3<4π/3
x=π/12 最大值2
x=π/2 最小值-√3