solve x*tan(x)-0.5=0

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rakesh kumar 2022-3-27

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https://ww2.mathworks.cn/matlabcentral/answers/1681919-solve-x-tan-x-0-5-0

编辑： Sam Chak 2022-3-28

I am again stuck with similar question which I asked earlier. I am trying to solve x*tan(x)-0.5=0,but when i cross checked the result I am getting very different results.

syms x
n=10;
for n = 1:2:n
x1 = (n-1/2)*pi;
x2 = (n)*pi;
w(n) = double(vpasolve(x*tan(x)-0.5 == 0,x,[x1 x2]))
check(n)=w(n)*tan(w(n))-0.5
end

I am getting

w =

1.5708 0 7.8540 0 14.1372 0 20.4204 0 26.7035

check =

1.0e+16 *

2.5653 0 2.5653 0 2.5653 0 -2.0830 0 -3.6311. I am unable to find my mistake.

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采纳的回答

Torsten 2022-3-27

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1681919-solve-x-tan-x-0-5-0#answer_928144

编辑：Torsten 2022-3-27

在 MATLAB Online 中打开

x1=0:0.1:1.3;
y1=x1.*tan(x1)-0.5;
x2=2:0.1:4.1;
y2=x2.*tan(x2)-0.5;
x3=5.5:0.1:6.9;
y3=x3.*tan(x3)-0.5;
plot(x1,y1,x2,y2,x3,y3)

So was your choice of x1 and x2 resonable ?

Here you get the asymptotic distribution of the zeros of your function in order to make a proper choice of x1 and x2:

https://math.stackexchange.com/questions/1238520/how-to-find-asymptotic-expansions-of-all-real-roots-of-x-tanx-epsilon-1

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rakesh kumar 2022-3-28

Thanks once again. I ran your code and its giving the perfect answer. You people are really great!

Sam Chak 2022-3-28

编辑：Sam Chak 2022-3-28

@Torsten

Learned something today. Thank you.

@rakesh kumar

Also thanks for showing an interesting question.

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