Which of the following best describes the shape traced by the curve with parametric equations $x=\sin \left(t\right)$, $y=3\sin \left(2t\right)$, $z=\sin \left(3t\right)$ as $t$ varies from $0$ to $2\pi$?

In Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = 2ᵗ, y = 2⁻ᵗ; t ≥ 0

In Exercises 59–62, sketch the plane curve represented by the given parametric equations. Then use interval notation to give each relation's domain and range. x = t² + t + 1, y = 2t

In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 7 − 4t, y = 5 + 6t; t = 1

In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = t² + 1, y = 5 − t³; t = 2

In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = t² + 3, y = 6 − t³; t = 2

In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 4 + 2 cos t, y = 3 + 5 sin t; t = π/2

Graph the plane curve formed by the parametric equations and indicate its orientation.

$x\left(t\right)=-t+1$;$y\left(t\right)=t^2$

$-2\le t\le 2$