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

1 Answer
Apr 19, 2018

"see explanation"

Explanation:

"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