Question

P

請問這要怎麼判斷 跪求詳解

(C) cos(-23°) + cos(217°) + cos(457°) > 0

Answer 1

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我就是我

為了方便，打字時省略「度」
觀察(217+457)/2=337=-23
cos(-23)+cos217+cos457
=cos337+(cos217+cos457)
=cos337+[2(cos-120)(cos337)] (和差化積公式)
=cos337[1+(2cos-120)]
=0

我就是我

cos-23+cos217+cos457
=cos337+cos217+cos97
=cos(330+7)+cos(210+7)+cos(90+7)
...
cos(330+7)=cos330cos7-sin330sin7
=根號3/2×cos7+1/2×sin7
cos(210+7)=cos210sin7-sin210cos7
=-根號3/2×sin7+1/2×cos7
cos(90+7)=-cos7
...
=0