ur cos θ + m/2π + (u sin θ) dr/dθ = 0 plot multiple solutions to this equation with m = 1 and u = 1. use the contour command to plot. in matlab

To plot multiple solutions to the equation cos θ + m/2π + (u sin θ) (dr/dθ) = 0 with m = 1 and u = 1 using the contour command in MATLAB, you can follow these steps:

1. Define the function f(θ) based on the given equation:

main.m
f = @(θ) cos(θ) + 1/(2*pi) + sin(θ);
37 chars
2 lines

2. Specify the range of values for θ over which you want to plot the solutions:

main.m
θ = linspace(-2*pi, 2*pi, 100);
32 chars
2 lines

3. Create a meshgrid of θ values and the corresponding values of f(θ):

main.m
[θ_mesh, f_mesh] = meshgrid(θ, f(θ));
38 chars
2 lines

4. Plot the contour lines of the equation using contour:

main.m
contour(θ_mesh, f_mesh, [0 0], 'LineWidth', 2);
48 chars
2 lines

This will plot the contour line corresponding to the equation cos θ + 1/(2π) + sin θ = 0.

5. Add labels and a title to the plot:

main.m
xlabel('θ');
ylabel('f(θ)');
title('Contour Plot of cos θ + 1/(2π) + sin θ = 0');
82 chars
4 lines

Here's the complete code:

main.m
f = @(θ) cos(θ) + 1/(2*pi) + sin(θ);
θ = linspace(-2*pi, 2*pi, 100);
[θ_mesh, f_mesh] = meshgrid(θ, f(θ));
contour(θ_mesh, f_mesh, [0 0], 'LineWidth', 2);
xlabel('θ');
ylabel('f(θ)');
title('Contour Plot of cos θ + 1/(2π) + sin θ = 0');
237 chars
8 lines

Running this code will generate a contour plot showing the solutions to the equation.