Question

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

A. r = 3sinθ
B. r = 3secθ
C. r = 3cscθ

Answer 1

C. r = 3cscθ

Step-by-step 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 = (3)/(\sin( \theta) )`

Recall that,

`\csc( \theta) = (1)/(\sin( \theta) )`

This implies that ,

`r = 3\csc( \theta)`

The correct choice is C