The rectangular equation that corresponds to the polar equation $r = 3 \csc \theta$ is

A)y = 3
B)x = 3
C)y = x
D)y = 3x
E)y = -3

Question

The rectangular equation that corresponds to the polar equation $r = 3 \csc \theta$ is

A)y = 3
B)x = 3
C)y = x
D)y = 3x
E)y = -3

Quizplus · Accepted Answer

The polar equation $r = 3 \csc \theta$ can be converted to rectangular coordinates by recognizing that $\csc \theta = \frac{1}{\sin \theta}$ and in polar coordinates, $\sin \theta = \frac{y}{r}$. Substituting these into the given equation gives $r = 3 \frac{1}{\sin \theta} = 3 \frac{r}{y}$, which simplifies to $y = 3$, corresponding to choice A.

The Rectangular Equation That Corresponds to the Polar Equation r=3csc⁡θr = 3 \csc \thetar=3cscθ

The Rectangular Equation That Corresponds to the Polar Equation $r = 3 \csc \theta$