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Exercise 28

Avg difficulty 2.5

For each of the following, describe the effect of the parameter ss on the parametric curve for tt in the interval [0,2π][0,2 \pi].

  1. r⃗(t)=⟨cos⁡(t),sin⁡(t)+s⟩\vr(t) = \langle \cos(t), \sin(t) + s \rangle

  2. r⃗(t)=⟨cos⁡(t)−s,sin⁡(t)⟩\vr(t) = \langle \cos(t)-s, \sin(t) \rangle

  3. r⃗(t)=⟨scos⁡(t),sin⁡(t)⟩\vr(t) = \langle s\cos(t), \sin(t) \rangle

  4. r⃗(t)=⟨scos⁡(t),ssin⁡(t)⟩\vr(t) = \langle s\cos(t), s\sin(t) \rangle

  5. r⃗(t)=⟨cos⁡(st),sin⁡(st)⟩\vr(t) = \langle \cos(st), \sin(st) \rangle

Long, Keller & Schlicker, Active Calculus Multivariable, §10.2 Vector-Valued Functions of One Variable, Exercise 28

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Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.