# Smooth curves

1. May 3, 2014

### Masgr404

1. The problem statement, all variables and given/known data

Determine where r(t) is a smooth curve for -pi <t<pi
R(t)= (x(t),y(t))=(4sin^3(t), 4cos^3(t))

2. Relevant equations

3. The attempt at a solution

To be honest I have no idea where to start. I know what a smooth function is but my understanding is that the sin(t) and cos(t) functions over all of t are smooth. No corners.
Any starting help would be appreciated.

2. May 3, 2014

### HallsofIvy

Yes, but you are NOT asked if sine and cosine are smooth- you are asked if F is smooth. What happens if the denominator of a fraction goes to 0? What fraction is involved here?

3. May 3, 2014

### Masgr404

The function is not continuous at that particular point that makes the denominator go to zero.
Perhaps we could rewrite in the complex plane?

4. May 3, 2014

### HallsofIvy

No, it is not necessary to work with the complex plane. What is the definition of "smooth curve"?

5. May 4, 2014

### LCKurtz

As someone on mathstackexchange said, a smooth curve is a curve with no stubble, like this:

#### Attached Files:

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Last edited: May 4, 2014