Re: Trigonometric equation????

*To*: mathgroup at smc.vnet.net*Subject*: [mg12983] Re: Trigonometric equation????*From*: Daniel Lichtblau <danl>*Date*: Sun, 28 Jun 1998 02:52:07 -0400*Organization*: Wolfram Research, Inc.*References*: <6mqf9u$3i1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Rikis wrote: > > I'm in trouble: I have to isolate x and y in this system of equations > and I don't know how... > > Could you please help me? > > L = C*x + (2*R) / tan(y/2) > > x = 2 * ( (V - R - R/cos(y)) * tan(y) ) > > L,C,R,V are constants > > Thank you very much!!! Playing around a bit I find that the following works. I believe the use of Together helped to avoid excessive complications caused by adding auxiliary variables and equations to handle denominators produced by TrigToExp. It also helps to have input that is in Mathematica InputForm. In[12]:= eqs = Together[TrigToExp /@ {-L + C*x + (2*R) / Tan[y/2], -x + 2 * ( (V - R - R/Cos[y]) * Tan[y])}]; In[13]:= Timing[sol = Solve[eqs==0, {x,y}];] Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found. Out[13]= {3.12 Second, Null} In[14]:= Length[sol] Out[14]= 5 In[15]:= LeafCount[sol] Out[15]= 10021 Playing some more, I find a method that avoids conversion to exponentials and also gives a simpler result, as measured in LeafCount. In[58]:= eqs = TrigExpand /@ {-L + C*x + (2*R) / Tan[z], -x + 2 * ( (V - R - R/Cos[2*z]) * Tan[2*z])}; In[59]:= Timing[sol = Solve[eqs==0, {x,z}] /. (z->a_) :> y->2*a;] Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found. Out[59]= {2.01 Second, Null} In[60]:= Length[sol] Out[60]= 5 In[61]:= LeafCount[sol] Out[61]= 706 In[62]:= sol[[1]] // InputForm Out[62]//InputForm= {x -> (L - 2*R*Root[-L + 2*R*#1 - 4*C*V*#1 + 2*L*#1^2 - 4*R*#1^3 - 8*C*R*#1^3 + 4*C*V*#1^3 - L*#1^4 + 2*R*#1^5 & , 1])/C, y -> 2*ArcCot[Root[-L + 2*R*#1 - 4*C*V*#1 + 2*L*#1^2 - 4*R*#1^3 - 8*C*R*#1^3 + 4*C*V*#1^3 - L*#1^4 + 2*R*#1^5 & , 1]]} Daniel Lichtblau Wolfram Research