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Re:公式的证明,不知对不对

Posted by 511818218 at 2013-09-24 16:28:25 on Problem 1031
In Reply To:Re:公式的证明,不知对不对 Posted by:chpzcc at 2012-06-04 14:24:30
> 设dl的一个端点为点A,一个端点为点B,点O(台灯)作垂直于该栅栏的线,交栅栏于点D,如下图:
> 
>     ————D——A—-—B—————  OA请自行想象...
> 	    |         /
>             |        /
>             |       / 
>             |      /
>             |     /
>             |    /
>             |   /
>             |  /
>             | /
>             |/
>             O
> 
> 有OB=r, 那么OD=r*cosa
> 设OA与OB的夹角为da,则,
> dl
> =AB
> =BD-AD
> =OD*(tana-tan(a-da))
> =r*(sina-cosa*(tana-tanda)/(1+tana*tanda))      //tan(a-b)公式
> =r*(sina*tana*tanda+cosa*tanda)/(1+tana*tanda)  //通分
> =r*tanda/(cosa+sina*tanda)                      //上下同乘cosa
> =r*sinda/(cosa*cosda+sina*sinda)                //上下同乘cosda
> =r*sinda/cos(a-da)
> =r*da/cos(a-da)                                 //sinda=da                                
> =r*da/cosa                                      //这步不知道是不是有点问题
> 
> 所以
> dI
> =I0*|cosa|*dl*h
> =k/r*|cosa|*r*da/cosa*h
> =k*h*da


用sinda不就完了干嘛要用tanda

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