Given the point with polar coordinates $(3,\frac{\pi }{4})$, which of the following polar coordinate pairs labels the same point?

Given the polar equation $r=6$, which of the following is the corresponding Cartesian equation?

Given the polar equation $r=9\cos \left(\theta \right)$, which of the following is its equivalent Cartesian equation?

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

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?

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

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