Given cos x = - 1/5 and x is in the third quadrant, match the trigonometric ratios with their respective values

tiles: (sin x) (-5/2sqrt6) (tan x) (1/2sqrt6) (csc x) (-2sqrt6/5) (sec x) (2sqrt6) (cot x)

First, we solve for x. Considering that it is in third quadrant, the value of x should be, 258.46°.

(1) sin 258.46° = - 0.98 = - 2sqrt6/5

(2) tan 258.46° = 4.90 = 2sqrt6

(3) csc 258.46° = 1/sin 258.46° = - 1.02 = - 5/2sqrt6

(4) sec 258.46° = 1/cos 258.46° = - 5

(5) cot 258.46° = 1/tan 258.46° = 0.20 = 1/2sqrt6