find sin theta if cot theta = -4 and cos theta <0

This means:



and



In what quadrant are cos and tan negative? When you found out this, make a quick sketch of a right angled triangle with angle theta, adjacent side 4, opposite side 1. Then use Pythagoras' Theorem to find the length of the hypotenuse.

Then,

The sign of your answer will depend on the quadrant you chose, and whether sin is positive or negative in that particular quadrant.