Parametric Equations: Graphs · Exercise 60

Use a graphing utility to graph the given parametric equations.
(a) $\{\begin{array}{l}x\left(t\right)=cost-1\\ y\left(t\right)=sint+t\end{array}$
(b) $\{\begin{array}{l}x\left(t\right)=cost+t\\ y\left(t\right)=sint-1\end{array}$
(c) $\{\begin{array}{l}x\left(t\right)=t-sint\\ y\left(t\right)=cost-1\end{array}$

The graph of each set of parametric equations appears to “creep” along one of the axes. What controls which axis the graph creeps along?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §10.7 Parametric Equations: Graphs · Exercise 60