solve trigonometrical equations with input range

How to solve on matlab this system trignometric? I need the code

1.42*cos(alfa)+3.3*cos(beta)+3.33*cos(gamma)-6= 0

1.42*sin(alfa)+3.3*sin(beta)+3.33*sin(gamma)=0

with alfa=linspace(19.7, -103, 14)

(19.7 and 103 are in degrees)

Answer 1

[Stephan]

Hi,

fsolve solves nonlinear systems. sind and cosd accept degrees as input arguments. Define your system like shown in the examples for fsolve and use a for loop to calculate the solutions for every needed value of alfa.

Best regards

Stephan

[pablolama]

can't you help me to write the code?

I0m not very able wuth Matlab,

Thanks a lot

[Stephan]

This is not the way things work here. Provide your attempts so far an ask a specific question to the problems you have by trying on your own.

[John D'Errico]

+1. Stephan is right on the money here. You don't learn MATLAB when someone gives you a complete answer that solves your problem. The main thing you do learn then is how to ask a question so that someone will do your thinking for you, the next time you find yourself even slightly over your head.

[John D'Errico]

@Pablolama - Please don't add an answer just to ask a question. Moved to a comment:

Why it doesn't work?

OA=1.42
AB=4.3
BO=3.33
oo=6
alfa=linspace(19.7, -103, 14)
syms OA AB alfa BO beta gamma 
Result=solve(OA*cosd(alfa)+AB*cosd(beta)+BO*cosd(gamma)-OO==0),...
    OA*sind(alfa)+AB*sind(beta)+BO*sind(gamma)==0,beta,gamma
Result.beta
Result.gamma

[madhan ravi]

Why ? see stephens answer carefully.

[pablolama]

I've used fsolve now... where i insert for loop?

[John D'Errico]

It fails first, because you overwrote all of your variables.

OA=1.42
AB=4.3
BO=3.33
oo=6
alfa=linspace(19.7, -103, 14)
syms OA AB alfa BO beta gamma 

so you created OA, AB, BO as double precision numbers. Then you re-defined them, when you created them as syms. The values they originally had when you created them? Those numbers diasppeared.

OA
OA =
OA

So now, OA, AB, and BO are all gone, turned into purely symbolic unknowns.

Next, you defined the variable oo. But then you use the variable OO.

And finally, you had a right parens in thewrong place.

OO= 6;
Result=solve(OA*cosd(alfa)+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...
    OA*sind(alfa)+AB*sind(beta)+BO*sind(gamma)==0,beta,gamma);

Basically, you need to learn to be more careful in your typing.

[pablolama]

This is correct?

OA=1.42
AB=4.3
BO=3.33
OO=6
alfa=linspace(19.7, -103, 14)

 
Result=fsolve(OA*cosd(alfa)+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...
    OA*sind(alfa)+AB*sind(beta)+BO*sind(gamma)==0,beta,gamma);
Result.beta
Result.gamma

[pablolama]

Thanks but when i insert:

OA=1.42
AB=4.3
BO=3.33
OO=6
alfa=linspace(19.7, -103, 14)

 
[res_beta, res_gamma]=solve([OA*cosd(alfa(k))+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...
OA*sind(alfa(k))+AB*sind(beta)+BO*sind(gamma)==0],beta,gamma);

i have:

Undefined function or variable 'k'.
Error in Untitled (line 8)
[res_beta, res_gamma]=solve([OA*cosd(alfa(k))+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...

[Stephan]

it is the counter variable of my for loop. Since you did not define a for loop there is an error message.

With every call of fsolve (or solve) i can get a solution for ONE discrete value of alfa. So the for loop should call fsolve (or solve) as often as there are different values for alfa to solve for.

[pablolama]

I've known the concept of for loop. In my case there are 14 repetitions... I'm not sure where and how to insert k=14

OA=1.42
AB=4.3
BO=3.33
OO=6
alfa=linspace(19.7, -103, 14)
k=14

[res_beta, res_gamma]=solve([OA*cosd(alfa(k))+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...
    OA*sind(alfa(k))+AB*sind(beta)+BO*sind(gamma)==0],beta,gamma);

[Stephan]

This will only use alfa at the index 14. You get one result. Where is the for loop?

[pablolama]

It is right this?

OA=1.42
AB=4.3
BO=3.33
OO=6
alfa=linspace(19.7, -103, 14)
for k=1:14
[res_beta, res_gamma]=solve([OA*cosd(alfa(k))+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...
    OA*sind(alfa(k))+AB*sind(beta)+BO*sind(gamma)==0],beta,gamma);
end

[pablolama]

Thanks man i've solved:

I have 28 results for beta and 28 results for gamma.

How can i select only the second of every results:

(360*atan((3*231145121043063523048193884227692741963912548529193598661322470324485271^(1/2))/3895915006802471275548707707929850169 + 448193734313188167693069702922240000/3895915006802471275548707707929850169))/pi
 -(360*atan((3*231145121043063523048193884227692741963912548529193598661322470324485271^(1/2))/3895915006802471275548707707929850169 - 448193734313188167693069702922240000/3895915006802471275548707707929850169))/pi

[Stephan]

it depends on how you saved them.

gamma = gamma(:,2) 

for example if you saved gamma as a 28x2 array.

[madhan ravi]

https://www.mathworks.com/help/matlab/ref/colon.html

[pablolama]

I'm really getting mad

2 minutes ago my code worked...

Now the same code pasted, doesn't work.

Suggest?

OA=1.42
AB=4.3
BO=3.33
OO=6
alfa=linspace(19.7, -103, 14)
for k=1:14
[res_beta, res_gamma]=solve([OA*cosd(alfa(k))+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...
    OA*sind(alfa(k))+AB*sind(beta)+BO*sind(gamma)==0],beta,gamma);
end





Not enough input arguments.

Error in beta (line 19)
y = exp(betaln(z,w));

Error in Untitled2222 (line 5)
[res_beta, res_gamma]=solve([OA*cosd(alfa(k))+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...

[Stephan]

syms beta gamma
OA=1.42;
AB=4.3;
BO=3.33;
OO=6;
alfa=linspace(19.7, -103, 14);
% preallocate solution arrays
result_beta = nan(numel(alfa),2);
result_gamma = nan(numel(alfa),2);
% solve and save the results
for k = 1:numel(alfa)
[res_beta, res_gamma]=solve([OA*cosd(alfa(k))+AB*cosd(beta)+BO*cosd(gamma)-OO==0,...
    OA*sind(alfa(k))+AB*sind(beta)+BO*sind(gamma)==0],beta,gamma);
result_beta(k,:)=double(res_beta);
result_gamma(k,:)=double(res_gamma);
end

[madhan ravi]

In your mind you know what is beta but matlab doesn’t know that so you have to tell it to matlab in the proper manner.

[pablolama]

One questions:

in results, i have:

It's evident that the first three rows are inverted (first column must be all negative, second all positive).... That it beacause of the angles and the equations. There is a way to invert them?

thanks

   56.3136  -68.0355
   60.0422  -66.3337
   63.3157  -63.8261
  -60.6513   65.9511
  -56.9882   67.8010
  -53.0279   68.7742
  -48.9467   68.8414
  -44.8871   68.0280
  -40.9515   66.3985
  -37.2048   64.0403
  -33.6824   61.0509
  -30.3996   57.5285
  -27.3598   53.5685
  -24.5623   49.2618

[Stephan]

quick and dirty:

gamma(1:3,:)=-gamma(1:3,:)

[pablolama]

<3

[pablolama]

Hi starting from this code, i have to derive equations to time, to find angular velocity...

Shoul i use DIFF command?