Find the exact value of cot ø if csc ø = -4/3 and and the terminal side of ø lies in quadrant iii

√7/3.

Step-by-step explanation:

csc Ø = 1 / sin Ø =  1 / -4/3 = -3/4.

As the sine is the opposite / hypotenuse  the side adjacent to angle Ø  will have length √(4^2 - 3^2) = √7 (by the Pythagoras theorem) and as  the angle is in the third quadrant this will be -√7.

So cot Ø = adjacent / opposite =  -√7/ -3

= √7/3   (answer).

Step-by-step explanation:

It is given that cosec =-4/3 and sin theta =1/cosec theta

so sin theta =-3/4 now since sin theta is perpendicular/hypotenuse, the third side base will be

and we know that cot theta is inverse of tan so it will be base/perpendicular

i.e and also it is given that side of theta is in quadrant III so cot theta will be positive, so final answer will be