Given the parametric equations $x=t\cos \left(t\right)$, $y=t$, $z=t\sin \left(t\right)$ for $t\ge 0$, which of the following best describes the graph of these equations?

Which of the following parametric equations represents a circle of radius $3$ centered at the origin, traced counterclockwise as $t$ increases from $0$ to $2\pi$?

Given the parametric equations $x=cos\left(8t\right)$, $y=sin\left(8t\right)$, $z=e^{0.8t}$, $t\ge 0$, which of the following best describes the graph of these equations?

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 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 = 3 − 5t, y = 4 + 2t; 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