Question

Find cot θ if csc θ = negative square root of thirty seven divided by six and tan θ > 0.

Answer 1

You can use the trigonometric identity  $1+\cot^2{x}=\csc^2{x}$.

$1+\cot^2{\theta}=(\frac{-\sqrt{37}}{6} )^2 \\ 1+\cot^2{\theta}=\frac{37}{36} \\ \cot^2{\theta}=\frac{1}{36} \\ \cot{\theta}=\frac{1}{6}$

The requirement that $\tan{\theta}\ \textgreater \ 0$ eliminates -1/6 from being another solution.