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[求助] 小女子公式求助，各位大神帮帮啦！已有3人参与

我有一个公式，需要求出x，s=2R*sin（x/2）+p*tan(x/2),各位大神这个该怎么求，谢啦！（s，R，p当做已知）

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追风的风(Edstrayer代发): 金币+2 2016-01-24 03:37:32

Matlab 的solve命令!
例如!
>> solve('2*sin(x/2)+3*tan(x/2)=2','x')

ans =

[    2*atan((2/3*(-3/4+1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+1/4*((6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)-9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^3+(-3/4+1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+1/4*((6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)-9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^2-1)/(-3/4+1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+1/4*((6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)-9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2)))]
[ 2*atan((2/3*(-3/4+1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-1/4*((6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)-9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^3+(-3/4+1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-1/4*((6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)-9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^2-1)/(-3/4+1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-1/4*((6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)-9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2)))-2*pi]
[ 2*atan(2/3*(-3/4-1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+1/4*i*((-6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)+9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^3+(-3/4-1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+1/4*i*((-6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)+9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^2-1,-3/4-1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+1/4*i*((-6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)+9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))]
[ 2*atan(2/3*(-3/4-1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-1/4*i*((-6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)+9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^3+(-3/4-1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-1/4*i*((-6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)+9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))^2-1,-3/4-1/4*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)-1/4*i*((-6*(315+72*19^(1/2))^(1/3)*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)*(315+72*19^(1/2))^(2/3)+9*(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2)+48*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3)/(((315+72*19^(1/2))^(2/3)+9+3*(315+72*19^(1/2))^(1/3))/(315+72*19^(1/2))^(1/3))^(1/2))^(1/2))]

>> double(ans)

ans =

0.7824
  -4.5525
5.0266 - 2.6622i
5.0266 + 2.6622i

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2楼2016-01-21 10:20:33

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liuqh

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【答案】应助回帖

★
感谢参与，应助指数 +1
追风的风(Edstrayer代发): 金币+1 2016-01-24 03:37:43

将sin(x/2)用tan(x/2)表示后，化简可得一个四次方程，有解析解

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3楼2016-01-21 10:38:24

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2楼: Originally posted by wurongjun at 2016-01-21 10:20:33
Matlab 的solve命令!
例如!
>> solve('2*sin(x/2)+3*tan(x/2)=2','x')

ans =

>> double(ans)

ans =

0.7824
-4.5525
5.0266 - 2.6622i
5 ...

可不可以结果出现R,s,p啊

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5楼2016-01-24 11:35:16

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这个可借助mathematica给出解析解的，但结果超复杂，这里没法全部粘贴出来...
试一下这个命令就可以看出结果了Solve[2 R Sin[x/2] + p Tan[x/2] == s, x]

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6楼2016-01-24 12:42:45

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w-chin

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结果文件这里，没法直接copy出来。话说为什么要解析解？http://pan.baidu.com/s/1i4zY14h

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7楼2016-01-24 12:50:17

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w-chin

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结果是nb格式，mathematica文件格式

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井蛙不可以语于海者，拘于虚也；夏虫不可以语于冰者，笃于时也；曲士不可以语于道者，束于教也。

8楼2016-01-24 12:51:27

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引用回帖:

7楼: Originally posted by w-chin at 2016-01-24 12:50:17
结果文件这里，没法直接copy出来。话说为什么要解析解？http://pan.baidu.com/s/1i4zY14h

我有另外一个公式，-t/（2Rθ）<=x2<=t/（2Rθ），我需要让我们s=2R*sin（x/2）+p*tan(x/2)的x>=x2，做出优化，优化p，使p小一些，这样怎么办啊？大神

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9楼2016-01-24 14:58:01

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5楼: Originally posted by 追风的风 at 2016-01-24 11:35:16

可不可以结果出现R,s,p啊...

不行!你说的那个叫解析解!
这个问题似乎只能求数值解!

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10楼2016-01-24 17:54:21

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