sin(2nπ+三分之二π)cos(nπ+三分之四π) n属于z的值
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sin(2nπ+三分之二π)cos(nπ+三分之四π) n属于z的值
sin(2nπ+2π/3)cos(nπ+4π/3)
n是奇函时
2n是偶数,
sin(2nπ+2π/3)cos(nπ+4π/3)
=sin(2π/3)[-cos(4π/3)]
=sin(2π/3)cos(π/3)
=√3/2*1/2
=√3/4
当n是偶数时
2n是偶数
sin(2nπ+2π/3)cos(nπ+4π/3)
=sin(2π/3)cos(4π/3)
=sin(2π/3)[-cos(π/3)]
=√3/2*(-1/2)
=-√3/4
综上
sin(2nπ+2π/3)cos(nπ+4π/3)=±√3/4
n是奇函时
2n是偶数,
sin(2nπ+2π/3)cos(nπ+4π/3)
=sin(2π/3)[-cos(4π/3)]
=sin(2π/3)cos(π/3)
=√3/2*1/2
=√3/4
当n是偶数时
2n是偶数
sin(2nπ+2π/3)cos(nπ+4π/3)
=sin(2π/3)cos(4π/3)
=sin(2π/3)[-cos(π/3)]
=√3/2*(-1/2)
=-√3/4
综上
sin(2nπ+2π/3)cos(nπ+4π/3)=±√3/4
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