The rectangular equation that corresponds to the polar equation $\theta = \frac { \pi } { 4 }$ is

A) $y = 4 x$
B) $4 y = x$
C) $y = - 4 x$
D) $y = x$
E) $y = - x$

Question

The rectangular equation that corresponds to the polar equation $\theta = \frac { \pi } { 4 }$ is

A) $y = 4 x$
B) $4 y = x$
C) $y = - 4 x$
D) $y = x$
E) $y = - x$

Quizplus · Accepted Answer

The polar equation $\theta = \frac{\pi}{4}$ represents a line that makes an angle of $\frac{\pi}{4}$ radians (or 45 degrees) with the positive x-axis in polar coordinates. When converted to rectangular coordinates, this corresponds to a line with a slope of 1, since tan($\frac{\pi}{4}$) = 1. Therefore, the equation of the line is $y = x$, which matches option D.

The Rectangular Equation That Corresponds to the Polar Equation θ=π4\theta = \frac { \pi } { 4 }θ=4π​

The Rectangular Equation That Corresponds to the Polar Equation $\theta = \frac { \pi } { 4 }$