How do you find the other five trigonometric values given cos x = 8/17 and tan x<0?

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Answer 1 · 2018-04-08T07:17:33

Please see below.

We have ,

#cosx=8/17 > 0toI^(st) and color(skyblue)(IV^(th) Quadrant....(1)#

Also, #tanx < 0toII^(nd) and color(skyblue)(IV^(th) Quadrant....(2)#

From #(1) and (2)#

#x in[(3pi)/2,2pi]...tocolor(skyblue)(IV^(th) Quadrant#

i.e. #sin,csc,tan,cot are(-ve) and sec is (+ve)#

So,

#(1)sinx=-sqrt(1-cos^2x)=-sqrt(1-64/289)=-15/17#

#(2)cscx=1/sinx=1/(-15/17)=-17/15#

#(3)tanx=sinx/cosx=(-15/17)/(8/17)==-15/8#

#(4)cotx=1/tanx=1/(-15/8)=-8/15#

#(5)secx=1/cosx=1/(8/17)=17/8#