2. The curve represented by the equation $\rho^{2} \sin \theta-\rho \cos ^{2} \theta-\sin \theta=0(\theta \in(0, \pi))$ in the Cartesian coordinate system is $\qquad$
Answer: $x=1 \cup\left(x^{2}+y^{2}+y=0(y \neq 0)\right)$
Difficulty: Easy
Examination: Polar coordinates, trigonometric functions
Analysis: $\rho^{2} \sin \theta-\rho \cos ^{2} \theta-\sin \theta=0$
$\Leftrightarrow(\rho \sin \theta-1)(\rho+\sin \theta)=0$
$\Leftrightarrow \rho \sin \theta=1$ or $\rho=-\sin \theta$
By $\theta \in(0, \pi), \rho \sin \theta=1 \Leftrightarrow x=1, \rho=-\sin \theta \Leftrightarrow x^{2}+y^{2}+y=0(y \neq 0)$