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 polar equation, getting $x = r = \cos\theta$. Squaring both sides of the equation $x^2 + y^2 = r^2$ (the Pythagorean theorem in polar coordinates) and substituting $r$ with $x$, we get $x^2 + y^2 = x$, which is choice A.

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

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