1. The problem statement, all variables and given/known data α(t) = (sint, cost + ln tan t/2) for α: (0:π) -> R2 Show that α is a smooth, parametrized curve, which is regular except for t = π/2 3. The attempt at a solution I am familiar with the definitions of smooth and regular, which I have provided below, however I am unsure as to how to formally show what the question asks. Am I supposed to show that dα/dt at t=π/2 is zero and hence not regular? for what it's worth, I have computed dα/dt at t=π/2 and it is = 0! Smooth - a function α(t) = α1(t), α2(t)....αn(t) is smooth if each of its components α1, α2,...,αn of α is smooth, that is, all the derivatives dαi/dt, d2α/dt2.... exist for i = 1,2,...,n Regular - a curve is regular if all its points are regular, that is dα/dt is nonzero.