Given that the polar equation r models the orbits of the planets about the sun,
-Suppose that a radio signal transmission pattern can be modeled by $r = 32 + 32 \sin \theta$, for $0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }$, where the units are miles. Assume that the positive $x$-axis points east, and determine the distances of transmission in the east, north, west, and south directions.
A) E: 32 miles, N: 32 miles, W: 32 miles, S: 0 miles
B) E: 64 miles, N: 32 miles, W: 0 miles, S: 32 miles
C) E: 32 miles, N: 64 miles, W: 32 miles, S: 0 miles
D) E: 32 miles, N: 0 miles, $W : 32$ miles, S: 64 miles

Question

Quizplus · Accepted Answer

To find the distances in each cardinal direction, we substitute the corresponding angle values into the equation $r = 32 + 32 \sin \theta$. For east ($\theta = 0^\circ$), $r = 32 + 32 \sin(0) = 32$ miles. For north ($\theta = 90^\circ$), $r = 32 + 32 \sin(90) = 64$ miles. For west ($\theta = 180^\circ$), $r = 32 + 32 \sin(180) = 32$ miles. For south ($\theta = 270^\circ$), $r = 32 + 32 \sin(270) = 0$ miles.

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