Find the polar equation for the curve represented by the given Cartesian equation. Select the correct answer.
$x + y = 2$
A) $r = 2 ( \cos \theta + \sin \theta )$
B)
$r = \frac { 1 } { \cos \theta - \sin \theta }$
C)
$r = \frac { 2 } { \cos \theta + \sin \theta }$
D)
$r = \frac { 2 } { \cos \theta - \sin \theta }$
E) $r = 1 ( \cos \theta + \sin \theta )$

Question

Quizplus · Accepted Answer

The Cartesian equation $x + y = 2$ can be converted to polar form using $x = r \cos \theta$ and $y = r \sin \theta$. Substituting these into the equation gives $r \cos \theta + r \sin \theta = 2$, which simplifies to $r = \frac{2}{\cos \theta + \sin \theta}$.

Find the Polar Equation for the Curve Represented by the Given