標題:

cos20 cos 40 cos80

發問:

aa.jpg

 

此文章來自奇摩知識+如有不便請留言告知

Without using the calculators, find the values of cos20 cos 40 cos80 Please explain to me

最佳解答:

This is a very good question. Make use of the fact that sin(2x) = 2 sin(x) cos(x), then sin(x) cos(x) = (1/2) sin(2x). Let S = cos20° cos 40° cos80°. S is what you want. Consider sin20° S = sin20°cos20° cos 40° cos80° = (1/2) sin40° cos 40° cos80° = (1/2)(1/2) sin80° cos80° = (1/2)(1/2)(1/2) sin160° = (1/2)(1/2)(1/2) sin(180° - 20°) = (1/2)(1/2)(1/2) sin20° S = (1/2)(1/2)(1/2) = 1/8 2013-08-23 00:44:03 補充: 其實這題已經出現在各大教科書之中了~ 都幾得意既~ 也要用到 sin(x) = sin(180° -x) 2013-08-23 22:26:31 補充: cf, 現時中學的課程,只有M2才會教double angle formula(即以前Additional Mathematics教的)。 你咁講即係你應該有讀M2,加油! =^o^=

其他解答:

這個方法M2書本應該有教過啦@@ 如果你看不出來,其實直接用product to sum一樣可以,不過較為麻煩。 cos20ocos 40ocos80o = ?(cos60o + cos20o)cos80o [i.e. cos60o = ?] = ?cos80o + ?cos20ocos80o = ?cos80o + ?(cos100o + cos60o) [i.e. cos100o = -cos80o] = ?cos60o = 1/8 //|||||勁~ M2都有教:D|||||Nice trick :)
arrow
arrow

    gbu94mz95e 發表在 痞客邦 留言(0) 人氣()