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+三分之二π)cos(nπ+三分之四π) n属于z的值](/uploads/image/z/19130931-27-1.jpg?t=sin%282n%CF%80%2B%E4%B8%89%E5%88%86%E4%B9%8B%E4%BA%8C%CF%80%29cos%28n%CF%80%2B%E4%B8%89%E5%88%86%E4%B9%8B%E5%9B%9B%CF%80%29+n%E5%B1%9E%E4%BA%8Ez%E7%9A%84%E5%80%BC)
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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