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

question 423

Multiple Choice

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 $$\mathrm { r } ^ { 2 } = \mathrm { k } \cos 2 \theta \text {, for } 0 ^ { \circ } \leq \theta \leq 360 ^ { \circ } ,$$ where the units are in miles. Describe the influence of k on the pattern. Assume that the positive x-axis points east.

• A) With increasing k, the distance of transmission becomes smaller in the east and west directions.
• B) With increasing k, the transmission becomes more strongly directed toward the east and less strongly directed to the west.
• C) With increasing k, the distance of transmission becomes greater in the east and west directions.
• D) With increasing k, the transmission becomes more strongly directed toward the north and less strongly directed to the east.