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Multiple answers from solve

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Kevin
Kevin il 5 Set 2021
Commentato: Kevin il 6 Set 2021
close all
clear
clc
AB=180
AO=60
BO=200
syms alpha
eqn1 = BO^2 == AB^2+AO^2-2*AB*AO*cosd(alpha)
eqn2 = solve (eqn1,alpha)
vpa(eqn2)
ans =
259.32807071423785412135760253313
100.67192928576214587864239746687
I know that it's the latter (100.6719....), but why does it give me 2 answers and how do I make matlab give me 1 answer?

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Walter Roberson
Walter Roberson il 5 Set 2021
AB=180
AB = 180
AO=60
AO = 60
BO=200
BO = 200
syms alpha
eqn1 = BO^2 == AB^2+AO^2-2*AB*AO*cosd(alpha)
eqn1 = 
sol = solve(eqn1, alpha)
sol = 
vpa(sol)
ans = 
How is MATLAB to know that one of the solutions is more right than the other?
You could vpasolve() with a range:
vpasolve(eqn1, alpha, [0 180])
ans = 
100.67192928576214587864239746687
  3 Commenti
Walter Roberson
Walter Roberson il 6 Set 2021
Yes, it means thare are two possible answers for alpha.
AB=180
AB = 180
AO=60
AO = 60
BO=200
BO = 200
syms alpha
eqn1 = BO^2 == AB^2+AO^2-2*AB*AO*cosd(alpha)
eqn1 = 
sol = solve(eqn1, alpha)
sol = 
vpa(sol)
ans = 
Now let us back-substitute the solutions into the defining equation
subs(eqn1, alpha, sol)
ans = 
lhs(ans) - rhs(ans)
ans = 
The difference between the two sides is 0, for both answers. So both answers are solutions. And MATLAB has no reason to know that one is "right" for your situation unless you give it more information to tell it which one you prefer.
Kevin
Kevin il 6 Set 2021
Thank you so much.

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