@Thomas Richard 

@Axel Vogt 

2) That depends on the expression and the range. I'll leave it to other to comment on specific examples. An interesting one was recently discussed here, but I don't have the link, sorry

It would be great if so can provide this link?

Thank you for your help

@Axel Vogt 

Due to the cos function, even if the equation is quiet simple, i think that you can not say that the equation is linear.

For the time dependency, we can suppress it because i observe my equation for a fixed time.

So we can considerer the equation without the time dependency as you can see below :

S1_eq5_psi[4] := -cos(gamma[0]+psi[4])*cr+sin(gamma[0])*lr-cos(-phi[4]+gamma[4])*mr-cos(gamma[4])*pr+z0-zp[4] = 0
solve({S1_eq5_psi[4],psi[4]>=-Pi/2,psi[4]<=Pi/2},psi[4]);

for the unknown psi[4], i look for solution with psi[4] belong to the range [-Pi/2,Pi/2].

For the parameters, cr>0, lr>0, mr>0, pr>0 are constant positive and z0 and zp[4] are reals.

I hope my solution will help to bring new ideas on this subject.

Thank you for your help

@Kitonum 

ok. thank you for your feedback.

However, I would like to keep complete symbolic equations. but, i could also precise ranges for the parameters. In this case, a>0 for example.

Do you have other ideas so that I can solve symbolic trigonometric equations if both variables and parameters have some domain definition ?

Here a more detail example of the kind of trigonometric equation that I would like to solve symbolically

S1_eq5_psi[4] := -cos(gamma[0](t)+psi[4](t))*cr+sin(gamma[0](t))*lr-cos(-phi[4](t)+gamma[4](t))*mr-cos(gamma[4](t))*pr+z0(t)-zp[4](t) = 0
solve({S1_eq5_psi[4],psi[4](t)>=-Pi/2,psi[4](t)<=Pi/2},psi[4](t));

Thank you for your help

@tomleslie 

perfect thank you

@tomleslie 

Perfect, it answers to my question.

The only point that I would need is to remove the brackets when there are more than 1 solutions.

I would like to obtain something like that sol1,sol2 instead of {sol1},{sol2}.

I have tried but without success with the op function.

May you help me to obtain the solution formatted as sol1,sol2, sol3 ... without the brackets ?

Thank you for your help

@vv 

Thank you for your help.

But, I find this solution not very convenient because the parameter linked to the slider and the one link to the textarea are not bound. Consequently, I think that it can lead to mistakes.

I would prefer a solution where the value of the parameter in the textarea and the one in the slider would be same. In other word, an altercation of the value in the textarea is taken into account in the slider or the contrary, a altercation of the slider is taken into account in the textarea.

Would you have other ideas ?

Thanks a lot for your help

@tomleslie 

I just try to run the code that acer send us : TestExplore_1.m

with this version of maple : `Maple 2016.1, X86 64 WINDOWS, Apr 22 2016, Build ID 1133417`

and i have the error mistake mentioned previously

@acer 

yes I have tried re-executing the whole sheet but I still obtain this error message which appears each time I try to drag a slider.

Here my version :

`Maple 2016.1, X86 64 WINDOWS, Apr 22 2016, Build ID 1133417`

Do you have other ideas ?

Thans a lot for your help

@acer 

Thank you acer.

I have MAple2016. It seems working but when I drag the slider i obtain this error message.

Do you have an idea of this problem and how can I troubleshoot it ?

@Kitonum 

OK I have tried but it seems that no simplifications is made with this function simplify(,size).

Do you have other ideas ?

Thanks a lot for your help

@Thomas Richard 

Hello,

Thanks a lot for your feedback

Here the new file :

TrigonometricSystem2.mw

The unknowns are mentioned in this new file :

ListAllUnknowns := [Psi(t), Theta[1](t), Theta[2](t), x[1](t), x[2](t), z[1](t), z[2](t)]

So it makes 7 equations with 7 unknowns variables.

The names that you have determined are parameters which are considered to be known.

Concerning your remark "I would use Worksheet mode for such applications, but that is a matter of preferences.", may you tell a bit more ? I'm interesting to progress on this field to have better presentation of my worksheet. Which mode do I use ? How can I change to the mode that you proposed. 

@acer 

@vv 

OK thank you for you help.

Now in this file

TrigEq3.mw

Is it possible to simplify again the last equation 5 but within preserving the following groups :

ListV := {cos(Psi(t)-Theta[1](t)), cos(Psi(t)-Theta[2](t)), cos(Psi(t)-Theta[3](t)), cos(Psi(t)-Theta[4](t)), cos(Psi(t)-gamma[1](t)), cos(Psi(t)-gamma[2](t)), cos(Psi(t)-gamma[3](t)), cos(Psi(t)-gamma[4](t)), cos(-phi[1](t)+gamma[1](t)), cos(-phi[2](t)+gamma[2](t)), cos(-phi[3](t)+gamma[3](t)), cos(-phi[4](t)+gamma[4](t)), cos(Psi(t)+phi[1](t)-gamma[1](t)), cos(Psi(t)+phi[2](t)-gamma[2](t)), cos(Psi(t)+phi[3](t)-gamma[3](t)), cos(Psi(t)+phi[4](t)-gamma[4](t)), cos(Psi(t)), sin(Psi(t)-Theta[1](t)), sin(Psi(t)-Theta[2](t)), sin(Psi(t)-Theta[3](t)), sin(Psi(t)-Theta[4](t)), sin(Psi(t)-gamma[1](t)), sin(Psi(t)-gamma[2](t)), sin(Psi(t)-gamma[3](t)), sin(Psi(t)-gamma[4](t)), sin(-phi[1](t)+gamma[1](t)), sin(-phi[2](t)+gamma[2](t)), sin(-phi[3](t)+gamma[3](t)), sin(-phi[4](t)+gamma[4](t)), sin(Psi(t))}

I only want the expand simplifications on these kind of groups :  (cos(a[1])-1)*(cos(a[1])+1) dealing with a[1], a[2], b[1], b[2]

Thank you for your help

@vv 

Perfect thank you

simplify didn't work but the simplfiy(expand( )) works well. For my culture, do you have ideas why ?

Moreover, in the same idea, may you see if you manage to simplify this other trigonometric equation 

TrigonometricEquation2.mw

The idea would be to simplfy only cos² () + sin²() = 1 but the simplify seems to expand the expression more than making the simplication  cos² () + sin²() = 1 

@acer 

Thank you for your interesting complement.

May you explain me the role of the option remember,system ?

@Doug Meade 

Perfect, it was exactly what I need