Solving a system of two trigonometric equations

[Thumpalumpacus]

So, in our Control Engineering classes, in the presentation about synthesizing a regulator using Bode plot (using lead compensation and lag compensation), we have the following system of equations:

omega_lb1 / omega_ln1 = 12.6
atan(2 / omega_lb1) - atan(2 / omega_ln1) = -6 deg

Allegedly, the solution is:

omega_lb1 = 0.2 rad/sec
omega_ln1 = 0.016 rad/sec

But how can that system of equations be solved?

Hi...are the equations written down exactly  as the problem is stated?   You must go back to the basic trigonometric definitions.  https://drive.google.com/file/d/16NotCY9...drive_link. This link will bring you to a pic of most of the solution.  Just apply the law of sines to the small isosceles triangle.  The solution should fall out.

OP has been banned, thread dead for a while.