Question

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

Answer 1

From cos<0 you get that theta is on the left side of the unit circle.
cot=1/tan and tan=sin/cos, so cot=cos/sin. From that you get that cos=-2sin, using the fact that cos^2+sin^2=1 you can substitute cos by a function of sin, and then isolate it to get its value.

Answer 2

Im so confused on what the answer is @ivanmlerner

Answer 3

Using the identity we get:\[\cos x=\sqrt{1-\sin^2 x}=-2\sin x\]Squaring everything we get:\[1-\sin^2 x=4\sin^2 x\]\[\sin x=\sqrt{\frac{1}{5}}\]Since the cot is negative the angle is on the upper side and the sin is positive