Use a graphing utility to graph the polar equation. Describe the resulting graph. $$r = 4 \cos ( 7 \theta - 2 )$$
A) rose curve with 7 petals, rotated 2 radians
B) rose curve with 7 petals, rotated 4 radians
C) lemniscate rotated 4 radians
D) limaçon rotated 4 radians
E) cardioid rotated 2 radians

Question

Quizplus · Accepted Answer

The polar equation $r = 4 \cos(7	heta-2)$ represents a polar rose with 7 petals, because the coefficient of $	heta$ is 7. The $-2$ in the argument of cosine means that the graph is rotated $2$ radians counterclockwise, but the question asks for the total rotation, which is $2$ radians. Therefore, the answer is (A) rose curve with 7 petals, rotated 2 radians.

Use a Graphing Utility to Graph the Polar Equation r=4cos⁡(7θ−2)r = 4 \cos ( 7 \theta - 2 )r=4cos(7θ−2)

Use a Graphing Utility to Graph the Polar Equation $r = 4 \cos ( 7 \theta - 2 )$