91Ó°ÊÓ

Sketch the graph of the given parametric equations; using a graphing utility is advisable. Be sure to indicate the orientation of the graph. \(x=\cos t, \quad y=\cos (2 t), \quad 0 \leq t \leq \pi\)

Find the values of \(\theta\) in the given interval where the graph of the polar function has horizontal and vertical tangent lines. \(r=\cos (2 \theta) ; \quad[0,2 \pi]\)

Graph the polar function on the given interval. \(r=1-\cos \theta, \quad[0,2 \pi]\)

Find \(t\) -values where the curve defined by the given parametric equations has a horizontal tangent line. \(x=\sqrt{t}, y=5 t+2\)

Sketch the graph of the given parametric equations; using a graphing utility is advisable. Be sure to indicate the orientation of the graph. \(x=\cos t, \quad y=\sin (2 t), \quad 0 \leq t \leq 2 \pi\)

Graph the polar function on the given interval. \(r=2+\sin \theta, \quad[0,2 \pi]\)

Find the values of \(\theta\) in the given interval where the graph of the polar function has horizontal and vertical tangent lines. \(r=1+\cos \theta ; \quad[0,2 \pi]\)

Find the equation of the parabola defined by the given information. Sketch the parabola. Vertex: (2,3)\(;\) directrix: \(x=4\)

Sketch the graph of the given parametric equations; using a graphing utility is advisable. Be sure to indicate the orientation of the graph. \(x=2 \sec t, \quad y=3 \tan t, \quad-\pi / 2

Find \(t\) -values where the curve defined by the given parametric equations has a horizontal tangent line. \(x=t^{2}-t, y=t^{2}+t\)