$\text { Find a polar equation in the form } r \cos \left( \theta - \theta _ { 0 } \right) = r _ { 0 } \text { for the given line. }$
-x = -4
A) $r \cos ( \theta + \pi ) = 4$
B) $\mathrm { r } \cos \left( \theta - \frac { \pi } { 2 } \right) = 4$
C) $r \cos \theta = 4$
D) $r \cos \left( \theta + \frac { \pi } { 2 } \right) = 4$

Question

$\text { Find a polar equation in the form } r \cos \left( \theta - \theta _ { 0 } \right) = r _ { 0 } \text { for the given line. }$
-x = -4 
A) $r \cos ( \theta + \pi ) = 4$
B) $\mathrm { r } \cos \left( \theta - \frac { \pi } { 2 } \right) = 4$
C) $r \cos \theta = 4$
D) $r \cos \left( \theta + \frac { \pi } { 2 } \right) = 4$

Quizplus · Accepted Answer

The line x = -4 can be represented in polar coordinates as $r \cos \theta = -4$. However, to match the given form $r \cos(\theta - \theta_0) = r_0$, we adjust the equation to $r \cos(\theta + \pi) = 4$, since $\cos(\theta + \pi) = -\cos(\theta)$.

Find a polar equation in the form rcos⁡(θ−θ0)=r0 for the given line. \text { Find a polar equation in the form } r \cos \left( \theta - \theta _ { 0 } \right) = r _ { 0 } \text { for the given line. } Find a polar equation in the form rcos(θ−θ0​)=r0​ for the given line.

$\text { Find a polar equation in the form } r \cos \left( \theta - \theta _ { 0 } \right) = r _ { 0 } \text { for the given line. }$