Find all other trigonometrical ratios if `s intheta=-(2sqrt(6))/5a n dtheta` lies in quadrant III.

Explanation

We have,
`cos^(2)+sin^(2)theta=1 rArr cos theta =+-sqrt(1-sin^(2)theta)`
In the third quadrant, cos`theta` is negative.
`therefore cos theta=-sqrt(1-sin^(2)theta) rArr costheta=-sqrt(1-24/25)=-1/5`
In the third quadrant, `tan theta` is positive
`tan theta =(sin theta)/(cos theta) rArr tan theta =(-2sqrt(6))/(5) x (-5/1) = 2sqrt(6)`
Now, `"cosec"theta=1/(sin theta) rArr "cosec"theta=-5/(2sqrt(6))`
`sec theta=1/(cos theta) rArr sec theta=-5`
And, `cot theta=1/("tan"theta) rArr cot theta =1/(2sqrt(6))`