分类：教育/科学-学习帮助
问题：不查表求三角函数值求cos5°+cos77°+cos149°+c 
求c5°+cos77°+cos149°+cos221°+cos293°的值。
回答：结果为0.
解：
(1)直接计算
`cos5°+cos77°+cos149°+cos221°+cos293°
=cos5°+cos77°-cos31°-cos41°+cos67°
=2cos41°cos36°-2cos36°cos5°+cos67
=2cos36°(cos41°-cos5°)+cos67°
=-2cos36°2sin23°sin18°+sin23°
=-sin23°(4sin18°cos18°cos36°)/cos18°+sin23°
=-sin23°(2sin36°cos36°/cos18°)+sin23°
=-sin23°(sin72°/sin72°)+sin23°
=-sin23+sin23
=0

(2)向量法
(cos5°,sin5°)+(cos77°,sin77°)+(cos149°,sin149°)+(cos221°,sin221°)+(cos293°,sin293°)=(0,0)