Find an equivalent equation in rectangular coordinates.
-$$\mathbf { r } = \cos \theta$$
A) $x ^ { 2 } + y ^ { 2 } = x$
B) $( x + y ) ^ { 2 } = y$
C) $( x + y ) ^ { 2 } = x$
D) $x ^ { 2 } + y ^ { 2 } = y$

Question

Quizplus · Accepted Answer

In polar coordinates, $r = \cos \theta$ can be converted to rectangular coordinates using the identities $x = r \cos \theta$ and $y = r \sin \theta$. Since $r = \cos \theta$, we substitute $r$ with $x$ in the equation $r^2 = x^2 + y^2$ (which comes from $r^2 = r^2(\cos^2\theta + \sin^2\theta)$), leading to $x^2 + y^2 = x$.

Find an Equivalent Equation in Rectangular Coordinates r=cos⁡θ\mathbf { r } = \cos \thetar=cosθ

Find an Equivalent Equation in Rectangular Coordinates $\mathbf { r } = \cos \theta$