If #tan x = -7/24#; and #cos x > 0#; find all possible trigonometric ratios?

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Answer 1 · 2018-05-13T08:20:43

Please see below.

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#