In Exercises 39 and 40, you will explore graphically the

Chapter 12, Problem 39CE

(choose chapter or problem)

In Exercises \(39\) and \(40\), you will explore graphically the behavior of the helix

\(r(t)=(\cos a t) i+(\sin a t) j+b t k\)

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

39.  Set \(b=1\). Plot the helix \(r(t)\) together with the tangent line to the curve at \(t=3 \pi / 2\) for  \(a=1,2,4 \text { and } 6\) over the interval \(0 \leq t \leq 4 \pi\). Describe in your own words what happens to the graph of the helix and the position of the tangent line as \(a\) increases through these positive values.

Equation Transcription:

Text Transcription:

39 and 40

r(t) = (cos at) i + (sin at) j + bt k

a

b

b=1

r(t)

t=3 pi / 2

a = 1, 2, 4 and 6

0 leq t leq 4