y=(3cosx+1)/(sinx+2)的值域

y=(3cosx+1)/(sinx+2)的值域
y=(3cosx+1)/(sinx+2)的值域

y=(3cosx+1)/(sinx+2)的值域
y=(3cosx+1)/(sinx+2)
ysinx+2y=3cosx+1
ysinx-3cosx=1-2y
√(y^2+9)sin(x+φ)=1-2y
则-1≤(1-2y)/√(y^2+9)≤1
解不等式得y∈[-2/3,2]

(-2,4/3)