Here,
#
(i)tanx=-7/24 < 0 =>II^(nd)Quadrant orcolor(blue)( IV^(th)Quadrant#
#(ii)# given that,#cosx > 0 =>I^(st) Quadrant or color(blue)( IV^(th) Quadrant#
From #(i) and (ii)# we can say that,
#(3pi)/2 < x <2pi=> color(blue)( IV^(th) Quadrant)=>cosx>0,secx >0#
#and sinx<0 ,cscx<0 ,tanx <0,cotx <0#
#(a) secx=sqrt((1+tan^2x))=sqrt(1+49/576)=sqrt(625/576)=25/24#
#(b)cosx =1/secx=1/(25/24)=24/25#
#(c)sinx=-sqrt(1-cos^2x)=-sqrt(1-576/625)=-7/25#
#(d)cscx=1/sinx =1/(-7/25)=-25/7#
#(e)cotx=1/tanx=1/(-7/24)=-24/7#