Question
Find $c$ so that one revolution about the $z$ axis of the helix gives an increase of $\Delta z$ in the $z$ -coordinate.$$x=2 \cos \pi t, y=2 \sin \pi t, z=c t, \Delta z=20$$
Step 1
Since x and y are given in terms of sine and cosine functions, one revolution occurs when the angle changes by 2π. In this case, the angle is given by πt, so we have: πt = 2π t = 2 Now, we know that after one revolution (t=2), the increase in the z-coordinate is Show more…
Show all steps
Your feedback will help us improve your experience
William Mead and 87 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find $c$ so that one revolution about the $z$ axis of the helix gives an increase of $\Delta z$ in the $z$ -coordinate. $$x=2 \cos t, y=2 \sin t, z=c t, \Delta z=15$$
Parameterization and Vector Fields
Parameterized Curves
Find $c$ so that one revolution about the $z$ axis of the helix gives an increase of $\Delta z$ in the $z$ -coordinate. $$x=2 \cos 3 t, y=2 \sin 3 t, z=c t, \Delta z=10$$
Find $c$ so that one revolution about the $z$ axis of the helix gives an increase of $\Delta z$ in the $z$ -coordinate. $$x=2 \cos t, y=2 \sin t, z=c t, \Delta z=50$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD