Given that the polar equation r models the orbits of the planets about the sun,
-Suppose that a radio transmission pattern can be modeled by $$r ^ { 2 } = 16,900 \sin 2 \theta , \text { for } 0 ^ { \circ } \leq \theta \leq 360 ^ { \circ } \text {, }$$ 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 and southwest; 16,900 miles
B) Northeast; 130 miles
C) Northeast and southwest; 130 miles
D) North and south; 130 miles

Question

Quizplus · Accepted Answer

The equation $r^2 = 16,900 \sin 2\theta$ represents a limaçon. The maximum transmission occurs when $\sin 2\theta = 1$, which happens at $\theta = 45^\circ$ (northeast) and $\theta = 225^\circ$ (southwest). Solving for $r$, we get $r = \sqrt{16,900} = 130$ miles.

Given That the Polar Equation R Models the Orbits of the Planets