Can someone help me how to calculate theta?

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Elham Rahimi
Elham Rahimi on 28 Oct 2021
Commented: Walter Roberson on 3 Nov 2021
a and b are variables calculated by measured values.
I dont know how should I define theta:
Unrecognized function or variable 'theta'.
S = solve ((((a+b)*theta)/(theta^2 - (a*b))*tan_theta), theta)
Walter Roberson
Walter Roberson on 1 Nov 2021
What happens if, hypothetically, theta were 0?
tan(theta) = (a+b) * theta /(theta^2 - a*b)
tan(0) is 0
0 = (a+b) * 0 / (0^2 - a*b)
0 = 0 * (a+b) /(-a*b)
if a*b is not 0 then the denominator is not 0. 0 / nonzero is 0. So left side is 0 and right side is 0.
Therefore theta = 0 is a solution whenever neither a nor b is 0.

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Answers (2)

Uba K Ubamanyu
Uba K Ubamanyu on 28 Oct 2021
try fsolve with an initial guess.
I am assuming you meant to write tan(theta) instead of tan_theta
intial_guess =1;
S = fsolve(@(theta) (((a+b)*theta)/(theta^2 - (a*b))*tan(theta)), initial_guess)
  1 Comment
Elham Rahimi
Elham Rahimi on 28 Oct 2021
I got this error!
No solution found.
fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.
<stopping criteria details>
Unrecognized function or variable 'theta'.
-- logically the equation should be solved for theta , I think basically something is wrong with my MATLAB code, which I cannt figure it out. fsolve is not working!

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Walter Roberson
Walter Roberson on 29 Oct 2021
The solution is theta = 0 unless a or b are 0.
Walter Roberson
Walter Roberson on 3 Nov 2021
eqn = str2sym('tan(theta) == (894987427786373*theta)/(4503599627370496*(theta^2 - 710587193844941/72057594037927936))')
eqn = 
E2 = lhs(eqn) - rhs(eqn)
E2 = 
fplot([E2, 0], [-1 1])

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