The cosmic origin of fluorine is still not well constrained. Several nucleosynthetic channels at different phases of stellar evolution have been suggested, but these must be constrained by observations. For this, the fluorine abundance trend with metallicity spanning a wide range is required. Our aim is to determine stellar abundances of fluorine for -1.1 < [Fe H] < +0.4. We determine the abundances from HF lines in infrared K-band spectra ( 2.3 mm) of cool giants, observed with the IGRINS and Phoenix high-resolution spectrographs. We derive accurate stellar parameters for all our observed K giants, which is important as the HF lines are very temperaturesensitive. We find that [F/Fe] is flat as a function of metallicity at [ F/Fe]0, but increases as the metallicity increases. The fluorine slope shows a clear secondary behavior in this metallicity range. We also find that the [F/ Ce] ratio is relatively flat for -0.6 < [Fe H] < 0, and that for two metal-poor ([Fe H] < - 0.8), s-process element-enhanced giants, we do not detect an elevated fluorine abundance. We interpret all of these observational constraints as indications that several major processes are at play for the cosmic budget of fluorine over time: from those in massive stars at low metallicities, through the asymptotic giant branch star contribution at -0.6 < [Fe H] < 0, to processes with increasing yields with metallicity at supersolar metallicities. The origins of the latter, and whether or not Wolf-Rayet stars and/or novae could contribute at supersolar metallicities, is currently not known. To quantify these observational results, theoretical modeling is required. More observations in the metal-poor region are required to clarify the processes there.