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

Explanation:

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

`(dr)/(d\theta)=(1)/(3)sin(3\theta)`

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

`(dr)/(d\theta)=0\\\\cos3\theta=0\\\\3\theta=(\pi)/(2)\\\\\theta=(\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=(\pi)/(6) \\\\\theta_2=(5\pi)/(6)\\\\\theta_3=(9\pi)/(6)=(3\pi)/(2)`

answer b