1. Given the parametrized curve (helix) a(9) = (a cos , a sin, b), seR, a(s) C C wodd where c² = a² +b², basitoineq a. Show that the parameter s is the arc length. b. Determine the curvature and the torsion of a. c. Determine the osculating plane of a. d. Show that the lines containing n(s) and passing through a(s) meet the z axis under a constant angle equal to 7/2. e. Show that the tangent lines to a make a constant angle with the z axis.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.4: Polyhedrons And Spheres
Problem 48E: Sketch the solid that results when the given circle of radius length 1 unit is revolved about the...
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Can you help me on "c"and"d" please ?

wun Cm » -
1. Given the parametrized curve (helix)
a(s) = (a cos, a sin b).
s e R,
where c² = a² +b²,
a. Show that the parameter s is the arc length.
b. Determine the curvature and the torsion of a.
c. Determine the osculating plane of a.
d. Show that the lines containing n(s) and passing through a(s) meet
the z axis under a constant angle equal to 7/2.
e. Show that the tangent lines to a make a constant angle with the z axis.
Transcribed Image Text:wun Cm » - 1. Given the parametrized curve (helix) a(s) = (a cos, a sin b). s e R, where c² = a² +b², a. Show that the parameter s is the arc length. b. Determine the curvature and the torsion of a. c. Determine the osculating plane of a. d. Show that the lines containing n(s) and passing through a(s) meet the z axis under a constant angle equal to 7/2. e. Show that the tangent lines to a make a constant angle with the z axis.
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