函数y=sin(x-π/3)+cos(x+7π/6)的最小值是多少

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/22 04:49:33
函数y=sin(x-π/3)+cos(x+7π/6)的最小值是多少函数y=sin(x-π/3)+cos(x+7π/6)的最小值是多少函数y=sin(x-π/3)+cos(x+7π/6)的最小值是多少y

函数y=sin(x-π/3)+cos(x+7π/6)的最小值是多少
函数y=sin(x-π/3)+cos(x+7π/6)的最小值是多少

函数y=sin(x-π/3)+cos(x+7π/6)的最小值是多少
y=sin(x-π/3)+cos(π+x+π/6)
=sin(x-π/3)-cos(x+π/6)
=sin(x-π/3)-sin[π/2-(x+π/6)]
=sin(x-π/3)-sin(π/3-x)
=sin(x-π/3)+sin(x-π/3)
=2sin(x-π/3)
所以最小值=-2

y=sin(x-π/3)+cos(x+7π/6)=1/2sinx-根号3/2cosx-根号3/2cosx+1/2sinx
=sinx-根号3cosx=2sin(x-π/3) 最小值是-2