The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).
-$$r = \cos \theta$$
A) $x ^ { 2 } + y ^ { 2 } = x$
B) $x ^ { 2 } + y ^ { 2 } = y$
C) $( x + y ) ^ { 2 } = y$
D) $( x + y ) ^ { 2 } = x$

Question

Quizplus · Accepted Answer

In polar coordinates, $x = r\cos\theta$ and $y = r\sin\theta$. Given $r = \cos\theta$, substituting $r$ in the equation $x^2 + y^2 = r^2$ gives $x^2 + y^2 = (\cos\theta)^2$. Since $x = r\cos\theta = (\cos\theta)^2$, the equation becomes $x^2 + y^2 = x$.

The Letters R and θ Represent Polar Coordinates r=cos⁡θr = \cos \thetar=cosθ

The Letters R and θ Represent Polar Coordinates $r = \cos \theta$