求函数y=2-3sinx/2+3sinx的值域

求函数y=2-3sinx/2+3sinx的值域
求函数y=2-3sinx/2+3sinx的值域

求函数y=2-3sinx/2+3sinx的值域
y=(2-3sinx)/(2+3sinx)
y' = [(2+3sinx)(-3cosx)-(2-3sinx)(3cosx)] /(2+3sinx)^2=0
-6cosx-9sinxcosx -(6cosx-9sinxcosx) =0
12cosx=0
x= π/2(max) or 3π/2(min)
max y = -1/5
min y = 5/(2-3)=-5
值域 = [-5,-1/5]