Question

find all triginometric values of θ with the given conditions
tan θ= -1, sin θ < 0
i know its in QIV and that cot θ = -1, but i get stuck there

Answer 1

I cant think of a way to solve this without having your unit circle memorized.
Maybe this might help a little?
\[\tan(\theta) = -1 \Longrightarrow \frac {\sin(\theta)}{\cos(\theta)} = -1 \Longrightarrow \sin(\theta) = -\cos(\theta)\]
So sin and cos should be the same number, just different signs.

Answer 2

and your right, its going to be in quadrant IV