Convert the following polar equation to rectangular form.
$$\theta = \frac { 2 \pi } { 3 }$$
A) $y = - \sqrt { 3 }$
B) $y = - \frac { \sqrt { 3 } } { 3 }$
C) $y = \sqrt { 3 }$
D) $y = - 3$
E) $y = \frac { \sqrt { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The polar equation $\theta = \frac{2\pi}{3}$ represents a line that makes an angle of $\frac{2\pi}{3}$ radians with the positive x-axis in the polar coordinate system. To convert this to rectangular form, we use the fact that $\tan(\theta) = \frac{y}{x}$. For $\theta = \frac{2\pi}{3}$, $\tan\left(\frac{2\pi}{3}\right) = -\sqrt{3}$, indicating a slope of the line in rectangular coordinates. However, since this equation represents a line at a constant angle, not a line with a slope in the Cartesian system, the direct conversion involves recognizing that this angle corresponds to a direction in the Cartesian plane but does not directly translate to a function $y = mx + b$. Instead, it indicates a direction from the origin. The correct conversion of a polar angle to a rectangular form doesn't result in an equation of a line in the form $y = mx + b$ but rather specifies a direction. However, none of the provided options correctly represent a conversion of the polar equation to a rectangular form in terms of creating a function of $x$ and $y$. The correct interpretation of the task, given the options, is not applicable as the angle $\theta = \frac{2\pi}{3}$ does not directly convert to a simple $y =$ equation in rectangular coordinates. My explanation was based on a misunderstanding of the task as presented.

Convert the Following Polar Equation to Rectangular Form θ=2π3\theta = \frac { 2 \pi } { 3 }θ=32π​

Convert the Following Polar Equation to Rectangular Form $\theta = \frac { 2 \pi } { 3 }$