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

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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?

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David Hill on 1 Apr 2020
So faz should be roughly equal to phase? What are you trying to do (big picture)?
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 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.

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 on 2 Apr 2020
Hi David,
Thank you for explaining everything very clearly. This worked really well for me!

### More Answers (1)

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.

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Guillaume on 1 Apr 2020
"How can I get 240 degrees output from this function?"
360 - acosd(x)
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 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 ?