Maximum and minimum curvature on the polar curve r = 3 + sin θ

[trap]

any clue?
Determine maximum and minimum values of the curvature at points of the polar curve r = 3 + sin $$\theta$$ .

 

[hypermorphism]

1. Find the curvature of the curve.
2. Use either intuition or calculus to find the extrema of the curvature.
Which step are you having trouble with ?

 

[trap]

so do I derive the curve and let it equal to zero to find the maximum? how about the minimum? also...I don't really get how do you find the curvature of the curve?

 

[amcavoy]

so do I derive the curve and let it equal to zero to find the maximum? how about the minimum? also...I don't really get how do you find the curvature of the curve?

$$\kappa=\frac{\left|\mathbf{r}'\times\mathbf{r}''\right|}{\left|\mathbf{r}'\right|^{3}}$$

here you can say r=<θ, 3+sinθ>

 

[trap]

$$\kappa=\frac{\left|\mathbf{r}'\times\mathbf{r}''\right|}{\left|\mathbf{r}'\right|^{3}}$$

here you can say r=<θ, 3+sinθ>

Sorry...I don't really get what you just typed, coz I don't think I have learned those in my course. We are currently doing parametric equations and polar coordinates. Is there an other approach to the question?

 

[amcavoy]

Sorry...I don't really get what you just typed, coz I don't think I have learned those in my course. We are currently doing parametric equations and polar coordinates. Is there an other approach to the question?

What I just typed was the vector form. Do you know about vectors from a previous course? Maybe precalc.?

 

[hypermorphism]

so do I derive the curve and let it equal to zero to find the maximum? how about the minimum? also...I don't really get how do you find the curvature of the curve?

See Mathworld - Curvature. You're probably looking for the extrinsic curvature of a curve in the plane.

 

[trap]

What I just typed was the vector form. Do you know about vectors from a previous course? Maybe precalc.?

no...we are not learning vectors

 

[trap]

See Mathworld - Curvature. You're probably looking for the extrinsic curvature of a curve in the plane.

yeah, something about the parametric, cartesian, polar equations are what we are learning. But I still don't get how to find the 'maximum' and 'minimum' values of the curvature.

 

[amcavoy]

yeah, something about the parametric, cartesian, polar equations are what we are learning. But I still don't get how to find the 'maximum' and 'minimum' values of the curvature.

Differentiate and set equal to zero!