# finding all roots of a trignometric equation

조회 수: 5(최근 30일)
pooja sudha 2020년 12월 30일
댓글: Ameer Hamza 2020년 12월 31일
Can we find all roots of a trignometric equation using matlab?
for e.g., tan(x)-x=0.

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### 답변(2개)

Ameer Hamza 2020년 12월 30일
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);
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Ameer Hamza 2020년 12월 31일
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

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Image Analyst 2020년 12월 30일
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

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