Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises - Page 617: 10

$r=2\csc \theta$ represents the horizontal line $y=2$.

We have $r=2\csc \theta\Longrightarrow r\sin\theta =2=y$. Also, $r=2\sec \theta\Longrightarrow r\cos\theta =2=x$. Since the horizontal line has the form $y=c$, then $r=2\csc \theta$ represents the horizontal line $y=2$.