If cotθ=2 and cosθ<0, how do you find sinθ?

1 Answer
Mar 30, 2018

Start with the identity:

1+cot2(θ)=csc2(θ)

Explanation:

Substitute cot2(θ)=(2)2:

1+(2)2=csc2(θ)

5=csc2(θ)

Substitute csc2(θ)=1sin2(θ)

5=1sin2(θ)

sin2(θ)=15

sin(θ)=±55

Because we are told that cos(θ)<0 and cot(θ)=2, we know that the sine function must be positive in this quadrant:

sin(θ)=55