Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 + 6 \sin \theta$
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$

Question

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 + 6 \sin \theta$ 
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $| r | = 8$ when $\theta = \frac { \pi } { 2 }$ $r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$

Quizplus · Accepted Answer

The graph of the polar equation $r=2+6\sin	heta$ is symmetric with respect to $	heta=\frac{\pi}{2}$ and $|r|=8$ when $	heta=\frac{\pi}{2}$. The equation also has zeros at $	heta=\frac{7\pi}{6}$ and $	heta=\frac{11\pi}{6}$. The only graph that satisfies all these conditions is graph B.

Select the Graph of the Polar Equation Using Symmetry, Zeros r=2+6sin⁡θr = 2 + 6 \sin \thetar=2+6sinθ

Select the Graph of the Polar Equation Using Symmetry, Zeros $r = 2 + 6 \sin \theta$