# Polar Curve question

1. Oct 2, 2005

### trap

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

2. Oct 2, 2005

### 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 ?

3. Oct 2, 2005

### 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?

4. Oct 2, 2005

### amcavoy

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

here you can say r=<θ, 3+sinθ>

Last edited: Oct 2, 2005
5. Oct 2, 2005

### trap

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?

6. Oct 2, 2005

### amcavoy

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

7. Oct 2, 2005

### hypermorphism

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

8. Oct 2, 2005

### trap

no...we are not learning vectors

9. Oct 2, 2005

### trap

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.

10. Oct 3, 2005

### amcavoy

Differentiate and set equal to zero!