Find the exact value of each trig value requested:?

Question

csc x=-2; x in QIV; cot x=?
tan x=3; x in QIII; sin x=?


I think i know the answer to the first one. The Tan would be -1/sqrt3 (you dont have to rationalize) so the cot would be -sqrt3/1 correct?
Thanks!

Answer 1

Cosecant is reciprocal sine, so the angle would be -30 degrees. So the cotangent would indeed be -sqrt(3). Sketching the second problem, the hypotenuse is sqrt(10), and the vertical side is 3, so the sine is 3/sqrt(10).

Answer 2

- sqrt(3) [the cot is negative QIV]

sin x = -3/sqrt(10) = -.3sqrt(10) {sin - in QIII}