Question

For what values of theta (0 less than or equal to theta less than or equal to 2pi) do maximum r values occur on the graph the polar equation r=4+3 sin3theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole.

Answer 1

Answer:

Step-by-step explanation:

To find the values of the angle which makes maximum r you use the derivative of r

$\frac{dr}{d\theta}=\frac{1}{3}sin(3\theta)$

If you equals this derivative to zero you obtain the value of the angle:

$\frac{dr}{d\theta}=0\\\\cos3\theta=0\\\\3\theta=\frac{\pi}{2}\\\\\theta=\frac{\pi}{6}$

However, the values of 5π/6 and 9π/6 are also available, because makes the sinusoidal function equal  to 1.

hence, the answer is:

$\theta_1=\frac{\pi}{6} \\\\\theta_2=\frac{5\pi}{6}\\\\\theta_3=\frac{9\pi}{6}=\frac{3\pi}{2}$

answer b