Find the value of other five trigonometric ratios: cotx = 3/4, x lies in third quadrant.

cotx=3/4 → tanx=1/cotx=4/3
Now 1+tan²x=sec²x → sec²x=1+(16/9) → sec²x=25/9
secx=±5/3
Since x lies in third quadrant, the value of secx will be negative.
∴secx=-5/3
cosx=1/secx=-3/5
tanx=sinx/cosx → sinx=(4/3)×(-3/5)=-4/5
∴cscx=1/sinx=-5/4