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] 下面是网上找的x∈[π/2,3π/2], x-π∈[-π/2,π/2], 又sin(x-π)=-sinx=-y 所以,x-π=arcsin(-y)=-arcsiny 即:x=π-arcsiny 从而y=sinx的反函数是:y=π-arcs...
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