Solving a system of two trigonometric equations

[LinuxGal]

FA, why won't you just do your own damned homework instead of asking others to do it for you? Cheating your way through school only hurts yourself.

What do you think is the point of school? The point of school is not to learn useful skills. The point of school is to give you a diploma, a piece of paper which is supposed to help you get hired.

[pjeuck]

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.  

Administrator Notice
Link removed per 30/30 rule.

 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.

[pjeuck]

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?

I worked it all out going back to fundamental trigonometric definitions.  It does work out to be a complex solution with a fourth order quadratic equation to solve.  I ran through the solution approach quickly and found it can be done.  I'll write it all out tomorrow and photograph it and then provide the link.  I will be going to a doctor so I might have it ready tomorrow but within a day to two I link the full solution.   You can't solve it like its a system of linear equations.  But the information given in the problem is enough.

[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.

[BrianSoddingBoru4]

Administrator Notice
Necroclosed.

Boru