# code for solution of 2 algebraic equations

GROUPS:
 hello dearsi am new to the mathematica forum as well as to using mathematica.i am a phd student and have developed a mathematical model, now needing the help of you guys in finding a solution2cos θ1 - 1.5sin θ1 = 0.08 ( (cos θ2)^2 )- 0.08( (sin θ2)^2 )+(.05)/θ1 (cos ( θ1/2))     (1)2sin θ1 + 1.5cos θ1 = 2(0.08 cos θ2 sin θ2)+ sin(θ1/2)                                   (2)This is a set of 2 equations with two unknowns, θ1 and θ2.If somebody can help me to solve this seemingly easy system but i have unsuccessfully tried a lot.Thanksif any body can help me
4 years ago
5 Replies
 Sean Clarke 1 Vote The first step is to write both equations in Mathematica's syntax. For example:2sin θ1+1.5cos θ1=2(.08cos θ2 sin θ2)+ sin(θ1/2)Should be:2 Sin[theta1]+ 1.5 Cos[theta1] == 2(0.08 Cos[theta2] Sin[theta2])+Sin[theta1/2] If you are new to using Mathematica, you will want a general overview before using it. Please see the Mathematica Virtual Book for an introduction to the correct syntax.Once you have both equations written out, you can try giving it to a function such as Solve or NSolve.
4 years ago
 Chip Hurst 3 Votes I don't think this system has a solution (over the reals). If we definef[θ_, ψ_] := 2 Cos[θ] - 1.5 Sin[θ] - 0.08 Cos[ψ]^2 + 0.08 Sin[ψ]^2 - 0.05 Cos[θ/2]/θg[θ_, ψ_] := 2 Sin[θ] + 1.5 Cos[θ] - 0.16 Cos[ψ] Sin[ψ] - Sin[θ/2]then we'd like to know where f[θ, ψ] == g[θ, ψ] == 0If we plot all three functions, it appears they don't simultaneously intersect.Plot3D[{f[x, y], g[x, y], 0}, {x, -10, 10}, {y, -10, 10}]
 Hi everyone, I am trying to solve 4 coupled algepraic equations...but seems like sth is wrong ... I wrote a code with Solve function but Mathematica seems like running but not getting the solution! I have 4 unknowns (k1,eps1,k2 and k12 other than these 4 are constant numbers) and 4 equations.. Thanks for any help! The code is: Solve[{((-Cmu*k1^2/eps1)^2*S^2) + (x12/taux12)*(-2*k1 + k12) - eps1 == 0, -Ceps2*eps1^2/k1 - Ceps1*2*S*k1 + 2*(Cmu*k1^2/eps1)^2*S^2 + Ceps3*(eps1/k1)*(x12/taux12)*(-2*k1 + k12) == 0, -1/taux12*(-2*k2 + k12) + (e^2 - 1)* k2/(3*dp*(Sqrt[2*Pi/3*k2])/(24*alpha2*g0)) == 0, -1/taux12*((1 + x12)*k12 - 2*x12*k2 - 2*k1) - k12/(Cmu* k1/eps1/Sqrt[ 1 + 0.45*(3*Ur^2/2*k1)]) - ((k12*(Cmu* k1/eps1/Sqrt[1 + 0.45*(3*Ur^2/2*k1)])*S^2)/3) == 0}, {k1, eps1, k2, k12}, Cubics -> False, Quartics -> False]