Question

If cot theta equals -3, and theta is in quadrant 2, what is sin theta?

Answer 1

\[1+\cot^2 x=\frac{1}{\sin^2x}\Rightarrow\sin x=\frac{+1}{\sqrt{1+\cot^2x}}\]
You select the positive sign, because the sin is positive in the second quadrant. To solve, you only have to substitute the cot x with -3, and you'll obtain,
\[\sin x=\frac{1}{\sqrt{10}}\]