You will explore graphically the behavior of the helix

as you change the values of the constants a and b. Use a CAS to perform the steps in each exercise.

Set a = 1. Plot the helix r(t) together with the tangent line to the curve at t = 3π/2 for b = 1/4, 1/2, 2, and 4 over the interval 0 ≤ t ≤ 4π. Describe in your own words what happens to the graph of the helix and the position of the tangent line as b increases through these positive values.

r(t) = (cos at)i + (sin at)j + btk