# Solving a set of trigonometric equations [closed]

I've been trying to solve the following equations in order to plot Subscript[θ, 41] with respect to Subscript[θ, 2] from 0 to 360 degrees. Subscript[r, 1] = 38.79;
Subscript[r, 2] = 15;
Subscript[r, 3] = 50;
Subscript[r, 41] = 41.5;
Subscript[θ, 1] = 191.6 Degree;

Eq1 = Subscript[r, 1] Cos[Subscript[θ, 1]] ==
(Subscript[r, 2] Cos[Subscript[θ, 2] \[Degree]] +
Subscript[r, 3] Cos[Subscript[θ, 3] \[Degree]] +
Subscript[r, 41] Cos[Subscript[θ, 41] \[Degree]])

Eq2 = Subscript[r, 1] Sin[Subscript[θ, 1]] ==
(Subscript[r, 2] Sin[Subscript[θ, 2] \[Degree]] +
Subscript[r, 3] Sin[Subscript[θ, 3] \[Degree]] +
Subscript[r, 41] Sin[Subscript[θ, 41] \[Degree]])

Plot[(Subscript[θ, 41] /.
NSolve[{Eq1, Eq2}, {Subscript[θ, 3], Subscript[θ, 41]}][]) + 360,
{Subscript[θ, 2], 0, 360} , PlotRange -> {{0, 360}, {240, 300}}]

Solution = (Subscript[θ, 41] /.
NSolve[{Eq1, Eq2}, {Subscript[θ, 3], Subscript[θ, 41]}][]) + 360;

Plot[Solution, {Subscript[θ, 2], 0, 360}]


The solution of this gives 4 solutions for Subscript[θ, 41]. The problem is, whenever I try to plot one of those solutions by putting the whole Solve phrase in the Plot statement, it works. But whenever I try to do them separately, it gives a completely different plot.

More details shown in the following photos: The first plot is the one I'm looking for. The second one gives a different plot!... Although I technically haven't done anything different.

I think it's important to mention that I've noticed that the strange plot I got (the second one) is somehow a combination of all 4 solutions. It's typical to a certain solution in a certain range of Theta's, then flips to another solution in another range. I don't know how this helps.

I hope someone would explain this to me, thank you !!

• Possibly the two plots are different due to the fact that Plot has attribute HoldAll or that it effectively is using Block for Theta2. – Karsten 7. Dec 11 '15 at 21:37
• @bbgodfrey The first plot produces something, because Subscript[\[Theta], 2] has a value at every point Plot evaluates that NSolve[...]. It is very similar to the situation here. – Karsten 7. Dec 12 '15 at 0:17