Convert the following polar equation to rectangular form. $$\theta = - \frac { 5 \pi } { 3 }$$
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 given polar equation $\theta = - \frac { 5 \pi } { 3 }$ specifies a direction but does not directly translate to a rectangular (Cartesian) equation involving x and y. However, the direction given by $\theta = - \frac { 5 \pi } { 3 }$ corresponds to a line that cannot be represented by a simple equation in x and y because it specifies an angle, not a relationship between x and y coordinates. The correct answer choice, A, mistakenly suggests a specific y-value, which does not directly follow from the conversion of the given polar equation. This indicates an error in the explanation process, as the conversion from a polar angle to a rectangular form does not yield a specific y-value without additional context such as a radius or a relationship to the x-coordinate.

Convert the Following Polar Equation to Rectangular Form θ=−5π3\theta = - \frac { 5 \pi } { 3 }θ=−35π​

Convert the Following Polar Equation to Rectangular Form $\theta = - \frac { 5 \pi } { 3 }$