Clear Filters
Clear Filters

Is it possible to make Acos return values greater than pi?

55 views (last 30 days)
I know the a, b and c and x values. I want to find Theta value. I use the command 'acos' for this, but 'acos' returns a value between [0, pi]. For example, it needs to return 240 degrees, but it retuns 120 deg. Since theta value is a phase shift, it is problematic. Any advice?
  6 Comments
Berke Ogulcan Parlak
Berke Ogulcan Parlak on 1 Apr 2020
What I really want to do is to give the system a sinusoidal input (A.sin (wt)) and find the frequency transfer function of the system by looking at the system's steady state output (A. | G (w) | .sin (wt + phase)). So I need to determine this phase and yes, 'faz' must be directly equal to phase.
David Hill
David Hill on 1 Apr 2020
I am still a bit confused. If you are only given C (sinusoidal input) how do you know what (a) and (c) are? If you know what A and B are, then you already know the (phase). Like I said before you could try all the possible solutions of (faz) and discard those that don't result in the equation equality.

Sign in to comment.

Accepted Answer

David Goodmanson
David Goodmanson on 2 Apr 2020
Edited: David Goodmanson on 2 Apr 2020
Hi Berke,
I wrote a clarification to your previous question which I think should resolve that issue. It looks like you have determined (or can determine) a, c and phi and wish to solve for b and theta. The first equation in your question is just the imaginary part of
a*exp(i*x) + b*exp(i*x + i*theta) = c*exp(i*x + i*phi)
Factoring out the exp(i*x) leaves
a + b*exp(i*theta) = c*exp(i*phi)
so the sum of two phasors is a third one. [ note that multiplying this equation by its complex counjugate gives the second equation in the question ]. Solving this gives
b = abs(c*exp(i*phi) - a)
theta = angle(c*exp(i*phi) - a)
Just like acos, angle has a convention that deals with 2pi ambiguity, which is -pi < angle <=pi. This means that for the case that you mentioned, angle will produce -120 degrees, not 240. That's how it is, but if you want only positive angles, then (for degrees) it would be mod(angle,360).
  1 Comment
Berke Ogulcan Parlak
Berke Ogulcan Parlak on 2 Apr 2020
Hi David,
Thank you for explaining everything very clearly. This worked really well for me!

Sign in to comment.

More Answers (1)

Guillaume
Guillaume on 1 Apr 2020
"Is it possible to make Acos return values greater than pi?"
No. The function codomain is mathematically defined as [0, π]. You can define your own reciprocal of the cosinus function with a different codomain but that won't be arccos.eg:
function y = myaccosd(x)
y = -accosd(x);
end
which would return your 240 degrees (mod 360) for an input of -0.5.
  4 Comments
Berke Ogulcan Parlak
Berke Ogulcan Parlak on 1 Apr 2020
What if the actual phase value is 120 degrees, then it will still get 240 degrees.
Walter Roberson
Walter Roberson on 1 Apr 2020
Edited: Walter Roberson on 1 Apr 2020
What information do you have that would permit you to distinguish whether 120 or 240 was the "actual" phase" ? And not (say) 600 ?

Sign in to comment.

Products


Release

R2016a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!