Solve the Problem $\mathrm { r } ^ { 2 } = 10,000 \sin 2 \theta$

Multiple Choice

Solve the problem.
-Suppose that a radio transmission pattern can be modeled by $\mathrm { r } ^ { 2 } = 10,000 \sin 2 \theta$ , for $0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }$ , where the units are miles. Determine the predominant direction(s) of transmission and the distance(s) of transmission in such direction(s) . Assume that the positive $x$ -axis points east.

A) Northeast; 100 miles
B) Northeast and southwest; 100 miles
C) North and south; 100 miles
D) Northeast and southwest; 10,000 miles