A carrier $Ac\cos(\omega c)t$ is frequency modulated by a signal $Em\cos(\omega m)t.$ The modulation index is $mf.$ The expression for the resulting FM signal is

$Ac\cos [\omega ct + mf\sin(\omega m)t]$

$Ac\cos [\omega ct + mf\cos(\omega m)t]$

$Ac\cos [\omega ct + \pi mf\sin \omega m t]$

$Ac\cos [\omega ct + 2\pi mf Em \cos(\omega m)t/\omega m]$