Is it possible to make Acos return values greater than pi?
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Berke Ogulcan Parlak on 1 Apr 2020
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?
David Goodmanson on 2 Apr 2020
Edited: David Goodmanson on 2 Apr 2020
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).
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);
which would return your 240 degrees (mod 360) for an input of -0.5.