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

Question

Quizplus · Accepted Answer

The equation $\mathrm{r}^2 = 10,000 \sin 2\theta$ represents a limaçon. The maximum value of $\sin 2\theta$ is 1, so $\mathrm{r}^2 = 10,000$ gives $\mathrm{r} = 100$. The angle $\theta$ for maximum transmission occurs when $2\theta = 90^\circ$ and $2\theta = 270^\circ$, corresponding to $\theta = 45^\circ$ (northeast) and $\theta = 135^\circ$ (southwest).

Solve the Problem r2=10,000sin⁡2θ\mathrm { r } ^ { 2 } = 10,000 \sin 2 \thetar2=10,000sin2θ

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