Given that $5\sin x\cos y+4\cos x\sin y=0$, and that $\cot x=2$, find the value of $\cot y$.
I don't understand why I got this question wrong. For this question, I drew a right-angled triangle. I then labelled angle $x$ and derived that 2 would be adjacent to $x$ and 1 would be opposite to $x$ because $\cot x=2=\frac21$. With both sides, I was able to work out the hypotenuse as $\sqrt5$.
I labelled angle $y$ as another angle in the right-angled triangle and then got $\cot y=\frac12$.