Replace the polar equation with an equivalent Cartesian equation.
-$$\mathrm { r } = - 7 \csc \theta$$
A) -7y = 1
B) y = -7
C) -7x = 1
D) x = -7

Question

Quizplus · Accepted Answer

The polar equation $r = -7\csc\theta$ can be converted to a Cartesian equation by recognizing that $\csc\theta = \frac{1}{\sin\theta}$ and in Cartesian coordinates, $\sin\theta = \frac{y}{r}$. Thus, substituting these into the equation gives $r = -\frac{7}{y/r}$, which simplifies to $r = -7y$. Since $r^2 = x^2 + y^2$ and in this context, we are looking for a direct relationship, we can simplify to $r = y$ when considering the vertical component directly. Therefore, the equation simplifies to $y = -7$, which matches choice B.

Replace the Polar Equation with an Equivalent Cartesian Equation r=−7csc⁡θ\mathrm { r } = - 7 \csc \thetar=−7cscθ

Replace the Polar Equation with an Equivalent Cartesian Equation $\mathrm { r } = - 7 \csc \theta$