Problems in solve iteratively calculation

Hi everyone, I'm newbie in Matlab. I'm trying to solve an equation iteratively, but the answer showed is different from my calculator.

syms dt2;
 
 solve((-2.4638*cos(dt2))-dt2 + 2.6628 == 0.0785,dt2)

The answer that I expect is 0.700201189 (I found it in my calculator), but I have 0.14711303119198522137688950797546 in Matlab.

Along with the answer, it shows a messagem:

 "Warning: Cannot solve symbolically. Returning a numeric approximation instead." 

[darova]

Use vpasolve

[Elisandro Peixoto]

Thank You!

Answer 1

[Ameer Hamza]

If you look at the graph of this equation, you can see that it has two solutions in the interval [0 1].

syms dt2;
f = (-2.4638*cos(dt2))-dt2 + 2.6628 - 0.0785;
fplot(f, [0 1])
yline(0)

MATLAB is not able to solve it analytically (probably such a solution does not exist for this equation), so you will need to a numerical method, e.g., vpasolve() or fsolve(). An easy way to get the required solution is to give an initial guess such that it is closer to the required root. For example

f = @(dt2) (-2.4638*cos(dt2))-dt2 + 2.6628 - 0.0785;
sol = fsolve(f, 1)

Result

sol =
    0.7002

[Elisandro Peixoto]

Thank You so much!

[Ameer Hamza]

I am glad to be of help.