Activity 10.2.2

The same curve can be represented with different parameterizations. Use appropriate technology to plot each of the curves generated by the following vector-valued functions for values of $t$ from $0$ to $2 \pi$. For each example, you should write a few sentences to explain how the graphs are alike and how they are different. Be sure to pay attention to how the parameter values are related to different points on the curve.

1. $\vr(t) = \langle \sin(t), \cos(t) \rangle$

2. $\vr(t) = \langle \sin(2t), \cos(2t) \rangle$

3. $\vr(t) = \langle \cos(t+\pi), \sin(t+\pi) \rangle$

4. $\vr(t) = \langle \cos(t^2), \sin(t^2) \rangle$