How to solve this system of nonlinear equations with parameters?

I've got some problems solving (numerically) this system of equations.

40⋅cos(2t)+105⋅cos(θ3)−75⋅cos(θ4)−91.924⋅cos(337.62(deg))=0 40⋅sin(2t)+105⋅sin(θ3)−75⋅sin(θ4)−91.924⋅sin(337.62(deg))=0

Now t is an array of numbers (variable?) ranging from 0 to 0.785 like this t = 0:0.01:0.785.

I was wondering if it is possible to find theta3 and theta4 for every t (like t=0 --> theta3=something, theta4=something...t=0.4-->theta3="something else", theta4="something else") put those values(solutions) in an array (vecotr)so that I can plot them.

I've tried to do it symbolically with solve but MATLAB couldn't find any (useful) solution. I tried to solve it numerically but I couldn't make it spit out more than two solutions at a time.

I'm new to MATLAB.

Answer 1

[Star Strider]

The new equations help!

This seems to work:

time = 0:0.01:0.785;
% T(1) = theta3,  T(2) = theta4
Eqsys2 = @(T,t) [40.*cos(2*t)+105.*cos(T(1))-75*cos(T(2))-91.924*cosd(337.62);  40*sin(2*t)+105*sin(T(1))-75*sin(T(2))-91.924*sind(337.62)];

for k1 = 1:length(time)
    t = time(k1);
    [Th, fv] = fsolve(@(T)Eqsys2(T,t), rand(1,2));
    Theta34(k1,:) = Th;
end

figure(1)
plot(time, Theta34(:,1),   time, Theta34(:,2))
legend('\Theta_3',  '\Theta_4', 'Location','NorthWest')
xlabel('t')
ylabel('\Theta')
axis([xlim  -pi pi])
grid

[Shaban]

Thank you very much for your reply Star Strider.I appreciate it a LOT because I was expecting only some tips on how to do it but you solved the most part of my problem. Thanks again. :)

[Star Strider]

My pleasure!

It was actually an interesting problem for me to work on. I developed it to the extent I did because I always test the code I post, and had problems getting it to work with arbitrary values for ‘theta1’. I wasn’t going to post it until I could get it to work satisfactorily, and your value for ‘theta1’ allowed that. Besides, if you’re new to MATLAB, a relevant example would be more helpful in your learning it than abstract hints.