tan x = -5/12, x lies in second quadrant. Find the values of other five trigonometric ratios.

tan x = -5/12 ⇒ cot x = 1/tan x = -12/5
Now using, 1 + tan²x = sec²x ⇒ sec²x = 1 + (-5/12)² = 1 + 25/144 = 169/144 ⇒ sec x = ±13/12
Since x lies in second quadrant, the value of sec x will be negative.
∴ sec x = -13/12
cos x = 1/sec x = -12/13
tan x = sin x / cos x ⇒ sin x = (tan x) × (cos x) = (-5/12) × (-12/13) = 5/13
∴ csc x = 1/sin x = 13/5