
Re: [中學] 1題三角函數請教~

: 毫無頭緒,想請教站上大師指點方向
: 感謝您,謝謝您,謝謝~
陳一理
假設的座標
較為好算
設A(0,3b),B(3a,0),C(0,0)
則內分點D(a,2b),E(2a,b)
cos(gamma)=6a^2/[(3a)sqrt(4a^2+b^2)]
=2a/[sqrt(4a^2+b^2)],sin(gamma)=b/[sqrt(4a^2+b^2)]
cos(alpha)=6b^2/[(3b)sqrt(a^2+4b^2)]
=2b/[sqrt(a^2+4b^2)],sin(alpha)=a/[sqrt(a^2+4b^2)]
cos(beta)=2(a^2+b^2)/[sqrt(a^2+4b^2)*sqrt(4a^2+b^2)]
sin(beta)=3ab/[sqrt(a^2+4b^2)*sqrt(4a^2+b^2)]
因而
[sin(gamma)sin(alpha)]/sin(beta)=ab/(3ab)=1/3 ...
--
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※ 編輯: wayne2011 (61.58.103.35), 08/27/2016 10:34:33
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