The popular amusement ride known as the corkscrew has a helical shape. The parametric equations for a circular helix are
x = a cos t
y = a sin t
z = bt
where a is the radius of the helical path and b is a constant that determines the “tightness” of the path. In addition, if b > 0, the helix has the shape of a right-handed screw; if b < 0, the helix is left-handed.
Obtain the three-dimensional plot of the helix for the following three cases and compare their appearance with one another. Use 0 ≤ t ≤ 10π and a = 1.
a. b = 0.1
b. b = 0.2
c. b = -0.1
