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標題:
cos20 cos 40 cos80
發問:
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 :)
cos20 cos 40 cos80
發問:
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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 :)
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