8.7 Parametric equations: graphs  (Page 3/4)

What are two methods used to graph parametric equations?

What is one difference in point-plotting parametric equations compared to Cartesian equations?

Why are some graphs drawn with arrows?

Name a few common types of graphs of parametric equations.

Why are parametric graphs important in understanding projectile motion?

$\{\begin{array}{l}x\left(t\right)=t\hfill \\ y\left(t\right)=t^2-1\hfill \end{array}$

$$\{\begin{array}{l}x\left(t\right)=t-1\hfill \\ y\left(t\right)=t^2\hfill \end{array}$$

$\{\begin{array}{l}x\left(t\right)=2+t\hfill \\ y\left(t\right)=3-2t\hfill \end{array}$

$\{\begin{array}{l}x\left(t\right)=-2-2t\hfill \\ y\left(t\right)=3+t\hfill \end{array}$

$\{\begin{array}{l}x\left(t\right)=t^3\hfill \\ y\left(t\right)=t+2\hfill \end{array}$

$\{\begin{array}{l}x\left(t\right)=t^2\hfill \\ y\left(t\right)=t+3\hfill \end{array}$

$\{\begin{array}{l}x(t)=t\\ y(t)=\sqrt{t}\end{array}$

$\{\begin{array}{l}x(t)=-\sqrt{t}\\ y(t)=t\end{array}$

$\{\begin{array}{l}x(t)=5-\left|t\right|\\ y(t)=t+2\end{array}$

$\{\begin{array}{l}x(t)=-t+2\\ y(t)=5-\left|t\right|\end{array}$

$\{\begin{array}{l}x(t)=4\text{sin}t\hfill \\ y(t)=2\cos t\hfill \end{array}$

$\{\begin{array}{l}x(t)=2\text{sin}t\hfill \\ y(t)=4\text{cos}t\hfill \end{array}$

$\{\begin{array}{l}x(t)=3{\cos }^{2}t\\ y(t)=\mathrm{-3}\sin t\end{array}$

$\{\begin{array}{l}x(t)=3{\cos }^{2}t\\ y(t)=\mathrm{-3}{\sin }^{2}t\end{array}$

$\{\begin{array}{l}x(t)=\sec t\\ y(t)=\tan t\end{array}$

$\{\begin{array}{l}x(t)=\sec t\\ y(t)={\tan }^{2}t\end{array}$

$\{\begin{array}{l}x(t)=\frac{1}{e^{2t}}\\ y(t)=e^{-t}\end{array}$

$\{\begin{array}{l}x\left(t\right)=t-1\hfill \\ y\left(t\right)=-t^2\hfill \end{array}$

$\{\begin{array}{l}x\left(t\right)=t^3\hfill \\ y\left(t\right)=t+3\hfill \end{array}$

$\{\begin{array}{l}x(t)=2\cos t\\ y(t)=-\sin t\end{array}$

$\{\begin{array}{l}x(t)=7\cos t\\ y(t)=7\sin t\end{array}$

$\{\begin{array}{l}x(t)=e^{2t}\\ y(t)=-e^t\end{array}$

$x=t^2,y=3t,0\le t\le 5$

$x=2t,y=t^2,-5\le t\le 5$

$x=t,y=\sqrt{25-t^2},0<t\le 5$

$x(t)=-t,y(t)=\sqrt{t},t\ge 0$

$x=-2\cos t,y=6\sin t,0\le t\le \pi$

$x=-\sec t,y=\tan t,-\frac{\pi }{2}<t<\frac{\pi }{2}$

Graph on the domain $\left[-\pi ,0\right],$ where $a=2$ and $b=1,$ and include the orientation.

Graph on the domain $\left[-\pi ,0\right],$ where $a=3$ and $b=2$ , and include the orientation.

Graph on the domain $\left[-\pi ,0\right],$ where $a=4$ and $b=3$ , and include the orientation.