Question

matlab求解这个方程组

100+a/2=173*cos(b)
sqrt(3)*a/2=173*sin(b）

Answer 1

用solve函数求解联立方程组：
[a,b]=solve('100+a/2=173*cos(b)','sqrt(3)*a/2=173*sin(b)','a','b')
a=simple(a)
b=simple(b)
a =
[ 1/2]
[-50 + 22429 ]
[ ]
[ 1/2]
[-50 - 22429 ]
b =
[ 1/2 1/2 ]
[ 3 (-50 + 22429 ) ]
[atan(---------------------)]
[ 1/2 ]
[ 150 + 22429 ]
[ ]
[ 1/2 1/2 ]
[ 3 (-50 - 22429 ) ]
[atan(---------------------)]
[ 1/2 ]
[ 150 - 22429 ]
a =
[ 1/2]
[-50 + 22429 ]
[ ]
[ 1/2]
[-50 - 22429 ]
b =
[ 1/2 1/2 ]
[ 3 (-50 + 22429 ) ]
[atan(---------------------)]
[ 1/2 ]
[ 150 + 22429 ]
[ ]
[ 1/2 1/2 ]
[ 3 (50 + 22429 ) ]
[atan(--------------------) ]
[ 1/2 ]
[ -150 + 22429 ]
>> a=eval(a)
b=eval(b)
a =
99.7631
-199.7631
b =
0.5229
-1.5701

追问

怎么把b的值表示成弧度或者角度的！谢谢！

追答

默认的都是弧度。若需表示成十进制角度，可将上述b值乘以换算系数（180度/π），带小数的。

Answer 2

使用solve命令呗，详细的可以百度一下solve命令！

Answer 3

clear all
close all
clc
[a,b]=solve('100+a/2=173*cos(b)','sqrt(3)*a/2=173*sin(b)','a','b')
a=simple(a)
b=simple(b)

a =

346*cos(-log(75/173 - (44858^(1/2)*(- 1 + 3^(1/2)*i)^(1/2))/346 - (25*3^(1/2)*i)/173)*i) - 200
346*cos(-log((44858^(1/2)*(- 1 + 3^(1/2)*i)^(1/2))/346 + 75/173 - (25*3^(1/2)*i)/173)*i) - 200

b =

-log(75/173 - (44858^(1/2)*(- 1 + 3^(1/2)*i)^(1/2))/346 - (25*3^(1/2)*i)/173)*i
-log((44858^(1/2)*(- 1 + 3^(1/2)*i)^(1/2))/346 + 75/173 - (25*3^(1/2)*i)/173)*i

a =

- 22429^(1/2) - 50
22429^(1/2) - 50

b =

atan((50*3^(1/2) + 67287^(1/2))/(22429^(1/2) - 150))
-atan((50*3^(1/2) - 67287^(1/2))/(22429^(1/2) + 150))

a=eval(a)
b=eval(b)

可以得到：
a =

1.0e+002 *

-1.9976 + 0.0000i
0.9976 - 0.0000i

b =

-1.5701 + 0.0000i
0.5229 + 0.0000i