y=根号3sin2x+3cos2x求值域

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/22 17:56:23
y=根号3sin2x+3cos2x求值域y=根号3sin2x+3cos2x求值域y=根号3sin2x+3cos2x求值域y=√3sin2x+3cos2x=2√3(1/2*sin2x+√3/2*cos2

y=根号3sin2x+3cos2x求值域
y=根号3sin2x+3cos2x求值域

y=根号3sin2x+3cos2x求值域
y=√3sin2x+3cos2x
=2√3(1/2*sin2x+√3/2*cos2x)
=2√3(cosπ/3sin2x+*sinπ/3cos2x)
=2√3sin(2x+π/3)
函数的值域是[-2√3,2√3]

因为aSinx+bCosx=根号(a2+b2)*Sin(x+y),
y=√[(√3)的平方+3的的平方](1/2*sin2x+√3/2*cos2x)
=2√3sin(2x+π/3)