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(Steps Shown) Consider the function f:R→ R^3 defined by f(θ)=(cos θ , sin θ ,θ) What kind of picture do you obtain when

Question: Consider the function \(f:\mathbb{R}\to {{\mathbb{R}}^{3}}\) defined by

\[f\left( \theta \right)=\left( \cos \theta ,\sin \theta ,\theta \right)\]
  1. What kind of picture do you obtain when you sketch the image of f in \({{\mathbb{R}}^{3}}\) ?
  2. Is this function continuous? You may assume that the elementary functions sin and cos are continuous.

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