10.7 Exercise 69

Use a graphing utility to graph the given parametric equations.

1. $\begin{cases} x \left(t\right) = \cos t - 1 \\ y \left(t\right) = \sin t + t \end{cases}$
2. $\begin{cases} x \left(t\right) = \cos t + t \\ y \left(t\right) = \sin t - 1 \end{cases}$
3. $\begin{cases} x \left(t\right) = t - \sin t \\ y \left(t\right) = \cos t - 1 \end{cases}$

Explain the effect on the graph of the parametric equation when we switched $\sin t$ and $\cos t$.