Answer:
A. pi/2, 7pi/6, 11pi/6
Step-by-step explanation:
When you graph it on your calculator you can see the points where the three petals hit.
The values of theta for which maximum r-values occur on the graph, for the polar equation r = 4 - 3 sin3 theta is Pi/6, 5pi/6, 3pi/2.
The polar coordinate system is the system in which the evert point on a two-dimensional plane is obtained by the radius from the origin point and angle from the reference direction.
The graph the polar equation given as,
[tex]r = 4 - 3 \sin(3 \theta)[/tex]
The maximum r-value occurs at a point that is the maximum distance from the pole. Differentiate the above equation with respect to the angle theta,
[tex]\dfrac{dr}{d\theta}= 0-9\cos(3 \theta)\\\dfrac{dr}{d\theta}= -9\cos(3 \theta)[/tex]
Equate this equation to the zero, to find the value of theta,
[tex]-9\cos(3 \theta)=0\\\cos(3 \theta)=0\\3\theta=\cos^{-1}0\\3\theta=\dfrac{\pi}{2}\\\theta=\dfrac{\pi}{6}[/tex]
For sinusoidal function equal to 1, the value of 5π/6 and 9π/6 or 3π/2 is also true.
Thus values of theta for which maximum r-values occur on the graph, for the polar equation r = 4 - 3 sin3 theta is Pi/6, 5pi/6, 3pi/2.
Learn more about the polar coordinates here;
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