Question

Find sin θ if cot θ = - 2 and cos θ < 0.

Answer 1

Draw a Right Triangle and label one acute angle \[\theta\]

Answer 2

Perfect. What's the definition of tangent or cotangent in a Right Triangle?

Answer 3

tan=opp/hyp and cot=inverse tan

Answer 4

No, no. Tangent is Opposite/Adjacent. Glad I asked.
Cotangent is NOT "inverse tangent". It's reciprocal tangent.

Okay, now we have COTANGENT is Adjacent/Opposite.
We also have, in the 1st Quadrant, that the cotangent is 2.
Lable the Opposite side "2" and the Adjacent side '1'.
Do you see why the labels are this way and why I switched to the 1st Quadrant?

Answer 5

No I'm sorry I dont know why we switched to the first quadrant.