Find the polar coordinates of the point(s) of intersection of the given curves for 0 ≤ θ

Question

Find the polar coordinates of the point(s) of intersection of the given curves for 0 ≤ θ < 2π.
-$$\mathrm { r } = 5 , \mathrm { r } = 5 + \sin \theta$$
A) $( 0,5 ) , ( \pi , 5 )$
B) $( 0,0 ) , ( 5,0 ) , ( 5 , \pi )$
C) $( 5,0 ) , ( 5 , \pi )$
D) $( 0,0 ) , ( 0,5 ) , ( \pi , 5 )$

Quizplus · Accepted Answer

The curves intersect where their equations are equal, so setting $r = 5$ equal to $r = 5 + \sin \theta$, we get $\sin \theta = 0$. This occurs at $\theta = 0$ and $\theta = \pi$, both with $r = 5$, corresponding to the points $(5,0)$ and $(5,\pi)$.

Find the Polar Coordinates of the Point(s) of Intersection of the Given