cos20°的值是多少?(不要用小數表示)

2009-07-14 10:38 pm
1.請教我這一題
4cos^3(10°)-3cos10°=cos3*10°=√3/2
求cos10°=?






2.或者也可以直接告訴我cos20°=?(不要用小數表示)



非常感謝你們!
更新1:

一般求cos20°精確值都是怎麼求的? 是用隸美弗公式嗎? 還是用三倍角公式? 只要告訴我cos20°精確值的詳細解法或是直接告訴我答案即可 至於「4cos^3(10°)-3cos10°=cos3*10°=√3/2 求cos10°=?」的這個問題不要管他 謝謝!

回答 (3)

2009-07-23 12:34 am
✔ 最佳答案
http://zh.wikipedia.org/wiki/%E7%B2%BE%E7%A1%AE%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E5%B8%B8%E6%95%B0#20.C2.B0

2009-07-22 16:34:27 補充:

圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant0.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant1.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant2.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant3.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant4.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant5.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant6.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant7.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant8.jpg


圖片參考:http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant9.jpg


http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant1.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant2.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant3.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant4.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant5.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant6.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant7.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant8.jpg
http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/trigonconstants/trigonconstant9.jpg


參考資料:
靈感來自http://hk.knowledge.yahoo.com/question/question?qid=7009051901805 + http://mathworld.wolfram.com/TrigonometryAnglesPi18.html + my wisdom of maths

2009-07-24 12:41:08 補充:
事實上,複數的立方根是irreducible,因為http://en.wikipedia.org/wiki/Casus_irreducibilis。
2009-07-15 5:34 pm
應該是用【泰勒展開式】來算近似值。不過會出現小數點,不合你的要求。

我用卡丹諾求3次方程式的方法算過4x^3-3x-√3/2=0,答案是x=cos10度,cos130度,cos250度,對求值來說沒幫助。

8x^3-6x-1=0的解我沒實際去算,不過我想應該也是cos10度,cos130度,cos250度,這三個沒什麼意義的答案吧。
2009-07-15 7:18 am
Yes...其實cos20度即是三次方程8x^3-6x-1=0的解


收錄日期: 2021-04-22 00:48:50
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090714000015KK05842

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