Consider the parametrization p(t) = (cos(t), sin(t), t) of the helix.

- At what times t does this intersect the sphere {(x, y, z) s.t. x² + y² + z² = 5}? (i.e. for what values of t is p(t) in the sphere?) Note: there are two intersections.

- Give a linear (constant velocity) parametrization of the tangent line to the helix at one of these points.

- Give a new parametrization of this tangent line with nonconstant velocity.