ANSWER
C. r = 3cscθ
EXPLANATION
The given Cartesian equation is:
[tex]y = 3[/tex]
The relation between Cartesian coordinates system and the polar coordinates system is:
[tex]x = r \cos( \theta) [/tex]
and
[tex]y= r \sin( \theta) [/tex]
Hence y=3 in polar coordinates is
[tex] r \sin( \theta) = 3[/tex]
Divide through by
[tex]\sin( \theta) [/tex]
[tex] r = \frac{3}{\sin( \theta) } [/tex]
Recall that,
[tex]\csc( \theta) = \frac{1}{\sin( \theta) } [/tex]
This implies that ,
[tex]r = 3\csc( \theta) [/tex]
The correct choice is C
