How to determine if a function is smooth?

Question

I want to figure out whether or not the following function is "Smooth". As far as I understand, a smooth function is means that it is C^∞

But how do I go about it with this function:

Let f : [0, π] → R^2 defined by f(t) = (sin(t)^2, cos2(t)^2).

Is f smooth?

Answer 1

Since each component is a $C^\infty$ function, $f$ is a $C^\infty$ function.