Convert the polar equation to rectangular form. $r = 4 \csc \theta$
A) $y = 4$
B) $y = 4 \mathrm { r }$
C) $x = 4$
D) $6 y = \mathrm { r }$
E) $x = 4 \mathrm { r }$

Question

Convert the polar equation to rectangular form.  $r = 4 \csc \theta$ 
A) $y = 4$
B) $y = 4 \mathrm { r }$
C) $x = 4$
D) $6 y = \mathrm { r }$
E) $x = 4 \mathrm { r }$

Quizplus · Accepted Answer

The equation $r = 4 \csc \theta$ can be converted to rectangular form by recognizing that $\csc \theta = \frac{1}{\sin \theta}$ and in polar coordinates, $\sin \theta = \frac{y}{r}$. Thus, $r = 4 \frac{1}{\sin \theta} = 4 \frac{r}{y}$, simplifying to $y = 4$.

Convert the Polar Equation to Rectangular Form r=4csc⁡θr = 4 \csc \thetar=4cscθ

Convert the Polar Equation to Rectangular Form $r = 4 \csc \theta$