Convert an Equation from Rectangular to Polar Coordinates
-$$x ^ { 2 } + y ^ { 2 } = 4$$
A) $\mathrm { r } = 2$
B) $r = 4$
C) $r ( \cos \theta + \sin \theta ) = 2$
D) $r ( \cos \theta + \sin \theta ) = 4$

Question

Quizplus · Accepted Answer

In polar coordinates, $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation $x^2 + y^2 = 4$ yields $r^2(\cos^2\theta + \sin^2\theta) = 4$. Since $\cos^2\theta + \sin^2\theta = 1$, this simplifies to $r^2 = 4$, or $r = 2$.

Convert an Equation from Rectangular to Polar Coordinates - x2+y2=4x ^ { 2 } + y ^ { 2 } = 4x2+y2=4

Convert an Equation from Rectangular to Polar Coordinates
- $x ^ { 2 } + y ^ { 2 } = 4$