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

Explanation

Given that `cotx=3/4` and x lies in third quadrant.
`cotx=3/4 rArr tan x=1/(cotx)`
`rArr tanx=1/(3//4) = 1 xx 4/3=4/3`
`therefore` x lies in third quadrant so, all ratio except tan and cot will be negative.
`therefore "cosec"^(2)x = 1+(3/4)^(2) = 1+9/16=25/16`
`rArr "cosec"x = -5/4`
`rArr sinx=1/(-5/4)= 1 xx (-4/5) =-4/5`
`cosx=(cosx)/(sinx). sinx`
`=cotx. sinx`
`=(3/4). (-4/5)`
`=-12/20 = -3/5`
`secx = 1/(cosx)=1/(-3/5) = 1 xx -5/3 -5/3`
Therefore, `sinx=-4/5, cosx=-3/5`
`tanx=4/3, "cosec"x=-5/4, secx =-5/3` Ans.