The polar equation of a circle is given. Give polar coordinates for the center of the circle and identify its radius.
-$$\mathrm { r } = 10 \sin \theta$$
A) $\left( 5 , \frac { 3 \pi } { 2 } \right)$, radius $= 5$
B) $C ( 5 , \pi )$, radius $= 5$
C) $\left( 5 , \frac { \pi } { 2 } \right)$, radius $= 5$
D) $C ( 5,0 )$, radius $= 5$

Question

Quizplus · Accepted Answer

The polar equation $r = 10 \sin \theta$ represents a circle with a radius of 5 units, centered at $\left( 5 , \frac { \pi } { 2 } \right)$ in polar coordinates. This is because the maximum value of $r$ is 10 when $\sin \theta = 1$, which occurs at $\theta = \frac{\pi}{2}$, and the radius of the circle is half the coefficient of $\sin \theta$, which is $5$.

The Polar Equation of a Circle Is Given r=10sin⁡θ\mathrm { r } = 10 \sin \thetar=10sinθ

The Polar Equation of a Circle Is Given $\mathrm { r } = 10 \sin \theta$