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,

$(3pi)/2 < x <2pi=> color(blue)( IV^(th) Quadrant)=>cosx>0,secx >0$

$and sinx<0 ,cscx<0 ,tanx <0,cotx <0$

$(a) secx=sqrt((1+tan^2x))=sqrt(1+49/576)=sqrt(625/576)=25/24$

$(b)cosx =1/secx=1/(25/24)=24/25$

$(c)sinx=-sqrt(1-cos^2x)=-sqrt(1-576/625)=-7/25$

$(d)cscx=1/sinx =1/(-7/25)=-25/7$

$(e)cotx=1/tanx=1/(-7/24)=-24/7$

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