How to solve expression containing trig, inverse trig and sqrt...

Thanks to reply,

Richard Fateman a écrit :

> You seem to have a NUMERICAL problem, not a symbolic
> problem.  Newton iteration might converge to a solution.
> A program was posted to this mailing list a few weeks ago.
> You can easily compute diff(f(t),t).
>
I know numerical algorithm and i'll use it if I failed but I can be
interesting for me to have a literal expression of the solution of

f(0, 0.04, 0.006, 62.5*%PI/180, 4, t, PHI , 0.029835)
- f(0.02, 0.06, 0.006, 62.5*%PI/180, 4, t+%PI/2, PHI, 0.029835)
= 0

i.e. t1=g(PHI), because my practical problem have at least 1 solution (I)

> As far as an exact symbolic solution, it doesn't look
> like a solution exists in closed form, though a proof of
> that is not obvious..

As we have faced to a practical problem, existence of the solution is
"known" (at least for some known value of PHI) but you're right, the
first problem to deal with is the existence of solutions...

> there might be some trick.  But
> Maxima does not do magic.  Just because you can ask a
> question does not mean there is an assurance of getting
> an answer.
>
It's true for every CAS...
That's the reason why I talk about my blackboard     ;-)
I do not ask Maxima does magic...

> Good luck!

>
> RJF
>
> Renaud AUBIN wrote:
>
>>
>> Hello,
>>
>> I'm a newbie and if the answer to my problem seems obvious, I'm sorry...
>>
>> I have a geometrical problem to solve, i.e. I want to know the planar 
>> parametric curve describes by a point submitted to geometrical 
>> constraints. I have already obtained the parametric equations [ 
>> fx(theta), fy(theta) ] but now, I want to solve fy(theta) - 
>> fy(theta+phi) = 0 but I did not succeed in using sequently 
>> trigexpand, trigsimp, trigreduce then solve...
>>
>> Is in maxima a special way to do that, or have I to return to my 
>> blackboard and try to solve my equation by myself ?
>>
>> Here is my f(t) :
>>
>> 0.029835*SIN(
>> ATAN2(0.006*SIN(4*t+0.97222222222222*%PI)
>> -0.006*SIN(4*t+0.34722222222222*%PI)
>> ,0.006*COS(4*t+0.97222222222222*%PI)
>> -0.006*COS(4*t+0.34722222222222*%PI)
>> +0.04)
>>
>> +ASIN(16.75884028825205*SQRT(
>> (0.006*SIN(4*t+0.97222222222222*%PI)
>> -0.006*SIN(4*t+0.34722222222222*%PI))^2
>> +(0.006*COS(4*t+0.97222222222222*%PI)
>> -0.006*COS(4*t+0.34722222222222*%PI)+0.04)^2)
>> )
>>
>> -%PI/2
>>
>> )
>> +0.006*SIN(4*t+0.34722222222222*%PI)
>>
>> When I try to solve f(t)-f(t+phi) = 0 , phi as a known value (i.e. 
>> two solutions exist) maxima does nothing than return to the next line 
>> with an input prompt...
>>
>>
>> Best regards,
>>
>>
>
>