y=sinx,则x∈[π/2,3π/2]
y=sinx=cos(π/2-x),则π/2-x∈[-π,0]
y=cos(π/2-x)=cos(x-π/2),则x-π/2∈[0,π],满足反余弦函数的定义域
令t=x-π/2,则y=cost
∴t=arccosy,即x-π/2=arccosy,即x=π/2+arccosy
∴反函数为y=π/2+arccosx,x∈[-1,1]