Replace the Cartesian equation with an equivalent polar equation.
-y = 10
A) $r = 10 \csc \theta$
B) $r = 10 \sec \theta$
C) $\mathrm { r } = 10 \sin \theta$
D) $r = 10 \cos \theta$

Question

Replace the Cartesian equation with an equivalent polar equation.
-y = 10 
A) $r = 10 \csc \theta$
B) $r = 10 \sec \theta$
C) $\mathrm { r } = 10 \sin \theta$
D) $r = 10 \cos \theta$

Quizplus · Accepted Answer

The Cartesian equation $y = 10$ represents a horizontal line 10 units above the x-axis. In polar coordinates, this line can be described by the equation $r = 10 \csc \theta$, where $\csc \theta = \frac{1}{\sin \theta}$ and $r\sin \theta = y$. This equation captures the relationship between the radius $r$ and the angle $\theta$ for points on the line $y = 10$.

Replace the Cartesian Equation with an Equivalent Polar Equation r=10csc⁡θr = 10 \csc \thetar=10cscθ

Replace the Cartesian Equation with an Equivalent Polar Equation $r = 10 \csc \theta$