Calculus: Other Calculus Problems – #28065

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

\[f\left( \theta \right)=\left( \cos \theta ,\sin \theta ,\theta \right)\]

(a) What kind of picture do you obtain when you sketch the image of f in \({{\mathbb{R}}^{3}}\) ?

(b) Is this function continuous? You may assume that the elementary functions sin and cos are continuous.

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