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

Question

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

Quizplus · Accepted Answer

The equation $r = 6 \csc \theta$ can be rewritten using the definition of $\csc \theta = \frac{1}{\sin \theta}$, which gives $r = \frac{6}{\sin \theta}$. Since $\sin \theta = \frac{y}{r}$ in polar coordinates, substituting this into the equation gives $r = \frac{6}{y/r}$, which simplifies to $y = 6$.

Convert the Polar Equation to Rectangular Form r=6csc⁡θr = 6 \csc \thetar=6cscθ

Convert the Polar Equation to Rectangular Form $r = 6 \csc \theta$