Let C be the curve parametrized by the vector-valued function R(t) = )= (-1+006 (1), (2, 3-sin()) 8 t√2 8 3 3 cos te that the curve C is smooth. 1. Find the unit tangent, unit normal, and unit binormal vectors to the curve C (with respect to the given parametrization) at the point where t = π. 2. Re-parametrize the curve C using the arc length from the point where t = 0 as the parameter.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Let C be the curve parametrized by the vector-valued function
t√2
8
- (-1+006 (1), V²,3-sin (1))
R(t) =
Note that the curve C is smooth.
1. Find the unit tangent, unit normal, and unit binormal vectors to the curve C (with respect to the given
parametrization) at the point where t = π.
2. Re-parametrize the curve C using the arc length from the point where t = 0 as the parameter.
Transcribed Image Text:Let C be the curve parametrized by the vector-valued function t√2 8 - (-1+006 (1), V²,3-sin (1)) R(t) = Note that the curve C is smooth. 1. Find the unit tangent, unit normal, and unit binormal vectors to the curve C (with respect to the given parametrization) at the point where t = π. 2. Re-parametrize the curve C using the arc length from the point where t = 0 as the parameter.
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