Analyzing a Smooth Curve for -π < t < π

[Masgr404]

Homework Statement

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

Homework Equations

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.

 

[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?

 

[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?

 

[HallsofIvy]

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

 

[LCKurtz]

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