How do i find roots for a trignometric function? eg (0.1*x)+10*tan(0.1*x)

The function roots does not work for this equation ?

Answer 1

[Star Strider]

Use the fzero function to get real roots. Plot it first, since it likely has several, and the initial estimate of the roots will reveal different values:

eqn = @(x) (0.1*x)+10*tan(0.1*x);
rt = fzero(eqn, 10)

rt =
    15.7080

[Nitesh Panchal]

what if i need to evaluate first 5 roots?

[Star Strider]

There are several ways, but the easiest would be to plot the function, get estimates for the roots from the plot, and then use a for loop with a vector of those estimates to get the values of the zeros. The advantage of the plot is that you see how the function behaves in your interval of interest, so that you know that there are five roots.

[Nitesh Panchal]

How do i plot this function with a for loop

[Star Strider]

You don’t plot it with a for loop, you use the plot to estimate the initial guesses for the parameter. If those initial guesses are for instance 0, 15, 30, ... (that seem appropriate here), you would write the loop as:

X0 = [0:15:15*4];
for k1 = 1:length(X0)
    rt(k1) = fzero(eqn, X0(k1));
end

x = linspace(1, 100);

figure(1)
plot(x, eqn(x))
hold on
plot(rt, zeros(size(rt)), 'or')
hold off
grid

Here, I plotted the function afterwards to demonstrate that it detected and estimated the first five positive zeros. The ‘rt’ vector has their locations.