The polar equation that corresponds to the rectangular equation $x - y = 0$ is

A) $r = \frac { 4 } { 2 \cos \theta + \sin \theta }$
B) $r = \tan \theta \sec \theta$
C) $r = \csc \theta \sec \theta$
D) $r ^ { 2 } = \frac { 4 } { 2 \cos ^ { 2 } \theta - \sin ^ { 2 } \theta }$
E) $\theta = \frac { \pi } { 4 }$

Question

The polar equation that corresponds to the rectangular equation $x - y = 0$ is

A) $r = \frac { 4 } { 2 \cos \theta + \sin \theta }$
B) $r = \tan \theta \sec \theta$
C) $r = \csc \theta \sec \theta$
D) $r ^ { 2 } = \frac { 4 } { 2 \cos ^ { 2 } \theta - \sin ^ { 2 } \theta }$
E) $\theta = \frac { \pi } { 4 }$

Quizplus · Accepted Answer

The rectangular equation $x - y = 0$ simplifies to $y = x$, which represents a line at a 45-degree angle to the x-axis. In polar coordinates, this corresponds to a constant angle of $\frac{\pi}{4}$ radians, or 45 degrees, hence the correct polar equation is $\theta = \frac{\pi}{4}$.

The Polar Equation That Corresponds to the Rectangular Equation x−y=0x - y = 0x−y=0

The Polar Equation That Corresponds to the Rectangular Equation $x - y = 0$