Proving a particle is traveling at constant speed
I have a particle traveling on a curve defined by (x,y) = r(t) where r(t) = (cos t, sin t, t)
I know this is a helix with the image being a circle, and I need to prove that the particle travels at a constant speed. I know grad r(t) will give me the tangent vector at a point ie (-sin t, cos t, 1). I thought that since grad gives rate of change, then a magnitude of 0 would mean constant speed. So trying this:
grad (cos t, sin t, t) = (-sin t, cos t, 1) and || (-sin t, cos t, 1)|| = root(2)..
meaning its not a constant speed right? But i know i'm wrong because my problem asks me to prove the speed is constant. CAn anyone advise please?