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

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Jim G.
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Apr 19, 2018

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#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)tan^2x+1=sec^2x#

#rArrsecx=+-sqrt(tan^2x+1)#

#•color(white)(x)sin^2x+cos^2x=1#

#rArrsinx=+-sqrt(1-cos^2x)#

#"Given "tanx<0" and "cosx>0" then"#

#"x is in the fourth quadrant"#

#tanx=-7/24rArrcotx=1/tanx=-24/7#

#secx=+sqrt((-7/24)^2+1)#

#color(white)(secx)=sqrt(49/576+1)=sqrt(625/576)=25/24#

#rArrcosx=1/secx=24/25#

#rArrsinx=-sqrt(1-(24/25)^2)#

#color(white)(rArrsinx)=-sqrt(1-576/625)=-sqrt(49/625)=-7/25#

#rArrcscx=1/sinx=-25/7#

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