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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.

For what values of theta (0 less than or equal to theta less than or equal to 2pi-example-1
User Kallakafar
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1 Answer

3 votes

Answer:

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

For what values of theta (0 less than or equal to theta less than or equal to 2pi-example-1
User Ardavan
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