Which of the following is a polar equation for the curve represented by the Cartesian equation $x^2+y^2=3$?

Find the exact length of the polar curve $r=2$ for $0\le \theta \le 2\pi$.

Which of the following correctly expresses the conversion from rectangular coordinates $(x,y,z)$ to cylindrical coordinates $(r,\theta ,z)$?

Given the polar equation $r=5\cos \left(\theta \right)$, which of the following is its Cartesian equation?

Given the polar equation $r=7\cos \left(\theta \right)$, which of the following is the corresponding Cartesian equation?

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 = √t, y = t − 1

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 = 1 + 3 cos t, y = 2 + 3 sin t; 0 ≤ t < 2π

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 = 2 + 3 cos t, y = 4 + 2 sin t; t = π

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 = (60 cos 30°)t, y = 5 + (60 sin 30°)t − 16t²; t = 2