已知sin(π+α)=-1/2,tan(π/2-α)=?

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已知sin(π+α)=-1/2,tan(π/2-α)=?已知sin(π+α)=-1/2,tan(π/2-α)=?已知sin(π+α)=-1/2,tan(π/2-α)=?sin(π+α)=-sinα=-

已知sin(π+α)=-1/2,tan(π/2-α)=?
已知sin(π+α)=-1/2,tan(π/2-α)=?

已知sin(π+α)=-1/2,tan(π/2-α)=?
sin(π+α)=-sinα=-1/2
=> sinα=1/2 ==> α=π/6 或者 α=π/6 或 α=5π/6
当 α=π/6时,π/2-α=π/2-π/6=π/3
所以tan(π/2-α)=tan π/3 =根号3
当 α=5π/6时,π/2-α=π/2-5π/6=-π/3
所以 tan(π/2-α)=tan(- π/3) =负根号3

根号3或者负根号3
求得角度是30度或者150度