The question is not clear but I will solve it for all the possible conditions.
If cosФ = - √37 ÷ 6
Which means,
Adjacent = - √37
Hypotenuse = 6
This is not possible because hypotenuse cannot be smaller.
If cosecФ = - √37 ÷ 6
Which means,
Opposite = 6
Hypotenuse = - √37
Using Pythagoras theorem,
Adjacent = (Hypotenuse)² - (Opposite)²
Adjacent = √{(- √37)² - (6)²}
Adjacent = √{(37 - 36}
Adjacent = √{(1}
Adjacent = 1
Now we have all the three sides of a right triangle, therefore, we can find out the value for cotФ.
That is;
cotФ = adjacent ÷ opposite
cotФ = 