Determining max and min pts of a polar curve

[KataKoniK]

Determine the maximum and minimum values of the curvature at points of the polar curve r = 3 + sin q.

I know that the polar curve, r = 3 + sin q is sort of similar to an upside down heart when graphed. However, I am not sure what to do when finding the maximum and minimum values of the curvature at points of r = 3 + sin q.

Thanks in advance.

 

[Fermat]

Determine the maximum and minimum values of the curvature at points of the polar curve r = 3 sin q.
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You want to find the max and min values of the curve, rather than the curvature, yes?
The curvature is the rate at which the slope is changing.

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I know that the polar curve, r = 3 sin q is sort of similar to an upside down heart when graphed
...

Sorry, but the polar curve you gave is just a circle, sitting on top of the x-axis with the y-axis passing through the middle of it.
What you described sounds like an epi-cycloid.

... However, I am not sure what to do when finding the maximum and minimum values of the curvature at points of r = 3 sin q.

Thanks in advance.

There are a couple of ways of doing this problem. You can just sketch, and label, the graph of the curve and simply state that, by inspection, from the Figure/sketch, the max and min points are such-and-such.

Or, you can use http://archives.math.utk.edu/visual.calculus/3/polar.1/.
Set dy/dx equal to zero and solve for the angle.

 

[KataKoniK]

Thanks. btw, how did you plot those graphs in graphmatica?

edit - I also realized I made a typo with the equation. It's suppose to be r = 3 + sin q and not r = 3 sin q.

 

[Fermat]

for the circle, just type in at the "function" window,

r = 3 + sin(t)

for the epi-cycloid, just type in at the "function" window,

x = 2sin(t) - sin(2t); y = -2cos(t) + cos(2t) {-pi,pi}

where the {-pi,pi}is the range.

If you hit F1 then type "parametric" in the index, then click on "Display", you'll get full info.