Suppose that $f:[0,180]\to[-1,1]$ given by $\theta\mapsto\cos\theta$
I wondered whether there was a notation for this domain, the principle values of a trig function?
For example we would use $\mathbb{R}$ for the domain of a function of real numbers.
I had thought it may be $\mathbb {\Theta}$ but the principle values for the trig functions are different. Maybe that's why there isn't such a notation?
I ask because I'd like to stress the function converts angles to real numbers. You input an angle $180^\circ$ and output the real number $-1$
Thanks in advance for any information
Edit Thanks for the comment, I hadn't considered that angles are dimensionless. Perhaps this is why there isn't such a notation? However I think the question still stands but perhaps worded differently. Is there a specific notation for those intervals of the real numbers that could be the domain of a trig function for example $[0,\pi] $?