The sinusoidal modulating wave

$m(t)=A_{m}cos(2f_{m}t)$

is applied to a phase modulator with phase sensitivity $k_p.$ The unmodulated carrier wave has frequency $f_c$ and amplitude $A_c.$

$($a$)$ Determine the spectrum of the resulting phase$-$modulated signal, assuming that the maximum phase deviation ${}_p=k_p{A}_m$ does not exceed $0\mathrm{.}3$ radians. $(1)$

$($b$)$ Construct a phasor diagram for this modulated signal, and compare it with that of the corresponding narrow$-$band FM signal.