For a curve c(t) such that c' (t) 0 for any t, we define: T(t) = c'(t)/||c' (t)|| to be its unit tangent vector. We say that a curve is parametrized by arclength if ||c' (t)|| = 1 for all t. If a curve is parametrized by arclength, then its curvature at c(t) is defined to be k = ||T' (t)||. 1 1. Check that the helix c(t) = (cos(t), sin(t), t) is parametrized by arc length. 2. Compute the curvature of the helix c(t). 3. Find a constant c so that s(t) = (R cos(ct), R sin(ct)) has unit speed. And then, show that the curve s(t) has constant curvature.