Applet: Parametrized helix
The vector-valued function $\dllp(t)=(\cos t, \sin t, t)$ parametrizes a helix, shown in blue. This helix is the image of the interval $[0,6\pi]$ (shown in cyan) under the mapping of $\dllp$. For each value of $t$, the red point represents the vector $\dllp(t)$. As you change $t$ by moving the cyan point along the interval $[0,6\pi]$, the red point traces out the helix.
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