How to know if the solution for this angle ϕ is in units of radians or degrees? I am studying out of interest a modelling approximation for a plectrum plucking a string (eg. guitar, piano, harpsichord) as given by these articles:

*

*http://recherche.ircam.fr/pub/dafx11/Papers/24_e.pdf (relevant part on page 3 of pdf)

*https://stacks.stanford.edu/file/druid:wp454hs7976/Jack%20Perng%20Thesis-augmented.pdf (relevant part on page 75 of pdf)

The model works roughly like this:

The string is represented here as the yellow circle in cross-section. The red part on the left is the component the plectrum is attached to that moves (moving upwards along the y-axis here). The black bendy part is obviously the plectrum.
$F_p$ (the force from the plectrum) can be broken down in terms of $x$ and $y$ vector components as per:


Where E is the Young's Modulus, I is moment of inertia, and L' is how far along the length of the plectrum the string is contacting.
The only trouble I'm having in understanding this model is concerning the units of $\phi$. Is this angle solution going to be in radians or degrees? In C++, sin and cos take radians by default and you have to convert degrees to radians first if working from degrees. So I need to know which one I'm getting from this equation for $\phi$.
Is $\phi$ here in radians or degrees?
Thanks for any guidance.

Oddly enough, the angle should usually be given in radians. However, looking at the first referenced paper, I am 99% sure that they are using angles in degrees. The authors speak of ( after (6) )

For small-angle approximations ($\phi<<1$), this reduces [...].

If this would be in radians, this would mean roughly 57° which is not really a "small-angle approximation".
Also, they say that

when $\theta=90°$, there is no bending [...].

Which also indicates the use of angles in degrees. I would suggest contacting the authors. Usually, authors are very happy if someone is interested in their work and are willing to help. You could also try to replicate the given results since the authors seem to have provided all necessary data.
