finding all roots of a trignometric equation
9 views (last 30 days)
Show older comments
Can we find all roots of a trignometric equation using matlab?
for e.g., tan(x)-x=0.
0 Comments
Answers (2)
Ameer Hamza
on 30 Dec 2020
range of tan(x) is (-inf inf), so this equation has an infinite number of solutions. Also, the solutions to this equation cannot be represented analytically. There is no general way to find multiple solutions to such equations. One solution is to start the numerical solver with several starting points and choose unique values. For example
eq = @(x) tan(x)-x;
x_range = 0:0.1:20;
sols = ones(size(x_range));
for i = 1:numel(sols)
sols(i) = fsolve(eq, x_range(i));
end
sols = uniquetol(sols, 1e-2);
2 Comments
Walter Roberson
on 30 Dec 2020
The solutions to tan(x)-x tend towards being close to 2*pi apart, so it is possible to generate reasonable starting points for as many points as desired until you start losing too much floating point precision.
However, you will never have enough memory to return them "all".
Ameer Hamza
on 31 Dec 2020
Yes, thats a good observation to give the initial points. The solutions are pi apart from each. Following will also give same result as one in the answer.
eq = @(x) tan(x)-x;
x_range = 0.1:pi:20;
sols = ones(size(x_range));
for i = 1:numel(sols)
sols(i) = fsolve(eq, x_range(i));
end
Image Analyst
on 30 Dec 2020
Well here's one way. Use fminbnd() to find out where the equation is closest to zero:
x = linspace(-1, 1, 1000);
y = tan(x);
plot(x, x, 'b-', 'LineWidth', 2);
hold on;
plot(x, y, 'r-', 'LineWidth', 2);
grid on;
axis equal
% Use fminbnd() to find where d = 0, which is where tan(x) = x.
xIntersection = fminbnd(@myFunc, -1.5,1.5)
% Put a line there
xline(xIntersection, 'Color', 'g', 'LineWidth', 3);
caption = sprintf('xIntersection = %f', xIntersection);
title(caption, 'FontSize', 20)
function d = myFunc(x)
d = abs(tan(x) - x);
end
You get
xIntersection =
-1.66533453693773e-16
0 Comments
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!