matlab求解 sin（x）=x*（1/3）的非0解

题目

matlab求解 sin（x）=x*（1/3）的非0解
要数值解或解析解；别画图；重谢

答案

>> syms x;f=inline('sin(x)-x*(1/3)')
f =
Inline function:
f(x) = sin(x)-x*(1/3)
>> fplot(f,[-10,10])
>> grid
由图像可以看出在[-4,-2]和[2,4]之间有两个非零解,所以使用下面两条命令
>> [xroot,y]=fsolve(f,[2,4],1e-5)
Optimization terminated:first-order optimality is less than options.TolFun.
xroot =
2.278862660075828 2.278862660076503
y =
1.0e-012 *
0 -0.663136212608606
>> [xroot,y]=fsolve(f,[-4,-2],1e-5)
Optimization terminated:first-order optimality is less than options.TolFun.
xroot =
-2.278862660076468 -2.278862660075828
y =
1.0e-012 *
0.629607477264926 0
注意这里最终结果xroot是最终的区间（精度为1e-5）,也就是说方程的根在[2.278862660075828 2.278862660076503]之间,y是把该值代入f得到的函数值.