How do solver a function for multiple values then graph it

So i have a 2 part problem, first i need to solve for theta 1 and theta 2 for the following functions

fl = 4 * cos(thetal) + 2 * cos(thetal + theta2);

f2 = 4 * sin(thetal) + 2 * sin(thetal + theta2);

where F1 = 6 and F2 = values from .1 to 3.6

then i need to graph the values of theta1 and theta2 with my .1 to 3.6 range

I tried doing this but i keep getting a empty graph, how can this be done ?

Answer 1

[Star Strider]

I would use the Symbolic Math Toolbox:

syms theta1 theta2 f2
Eqn1 = 6 == 4 * cos(theta1) + 2 * cos(theta1 + theta2);
Eqn2 = f2 == 4 * sin(theta1) + 2 * sin(theta1 + theta2);
[th1,th2] = solve(Eqn1, Eqn2, [theta1, theta2]);

th1 =
  2*atan((8*f2 + f2^3/(- f2^2 - 32)^(1/2) + (32*f2)/(- f2^2 - 32)^(1/2))/(f2^2 + 96))
 -2*atan((f2^3/(- f2^2 - 32)^(1/2) - 8*f2 + (32*f2)/(- f2^2 - 32)^(1/2))/(f2^2 + 96))

th2 =
 -2*atan(f2/(- f2^2 - 32)^(1/2))
  2*atan(f2/(- f2^2 - 32)^(1/2))

[Shabib Abu-Jaber]

And then how do i plot it ?, and they have to both be in the same box

[Star Strider]

You create expressions or functions for each of them, remembering to vectorise them, then evaluate them for your values of ‘f2’. Then plot them as functions of your ‘f2’ vector. See the documentation for the plot function to understand how to plot them.

See the documentation for Array vs. Matrix Operations for details on how to write them to evaluate them with your ‘f2’ vector.

[Shabib Abu-Jaber]

And at start (before I enter the equation)I give f2 = linspace(.1,3.6, 35)??

[Star Strider]

That would work. Give it a go!