Question

Convert the Cartesian equation y = 3 to a polar equation.

Answer 1

ANSWER

C. r = 3cscθ

EXPLANATION

The given Cartesian equation is:

$y = 3$

The relation between Cartesian coordinates system and the polar coordinates system is:

$x = r \cos( \theta)$

and

$y= r \sin( \theta)$

Hence y=3 in polar coordinates is

$r \sin( \theta) = 3$

Divide through by

$\sin( \theta)$

$r = \frac{3}{\sin( \theta) }$

Recall that,

$\csc( \theta) = \frac{1}{\sin( \theta) }$

This implies that ,

$r = 3\csc( \theta)$

The correct choice is C