In words, describe the curve r(t) = (t, t, t sin t) for 0 ≤ t ≤ 8pi. (b) Given r(t) = (t^3, t^2, t), find a such that (−2, −1, a) is a point on the tangent line to the curve at t = 1. (c) True, False, or Indeterminate: The torsion of the curve r(t) in part (a) is zero

In words, describe the curve r(t) = (t, t, t sin t) for 0 ≤ t ≤ 8pi. (b) Given r(t) = (t^3, t^2, t), find a such that (−2, −1, a) is a point on the tangent line to the curve at t = 1. (c) True, False, or Indeterminate: The torsion of the curve r(t) in part (a) is zero

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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Question

a) In words, describe the curve r(t) = (t, t, t sin t) for 0 ≤ t ≤ 8pi.

(b) Given r(t) = (t^3, t^2, t), find a such that (−2, −1, a) is a point on the tangent line to the curve at t = 1.

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Step 1: Describing the curve

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Step 2: Calculating the point a

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Step 3: Calculating the torsion for curve in part (a)

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