91Ó°ÊÓ

Find an equation in polar coordinates that has the same graph as the given equation in rectangular coordinates. $$ x^{2}+y^{2}=5 \Rightarrow $$

Sketch the curve described by \(x=t^{3}-t, y=t^{2}\). If \(t\) is interpreted as time, describe how the object moves on the curve.

Find an equation in polar coordinates that has the same graph as the given equation in rectangular coordinates. $$ y=x^{3} \Rightarrow $$

A wheel of radius 1 rolls along a straight line, say the \(x\) -axis. A point \(P\) is located halfway between the center of the wheel and the rim; assume \(P\) starts at the point \((0,1 / 2) .\) As the wheel rolls, \(P\) traces a curve; find parametric equations for the curve. \(\Rightarrow\)

Find the area enclosed by the curve. $$ r=4+3 \sin \theta \Rightarrow $$

A wheel of radius 1 rolls around the outside of a circle of radius 3. A point \(P\) on the rim of the wheel traces out a curve called a hypercycloid, as indicated in figure 10.4 .3 . Assuming \(P\) starts at the point \((3,0),\) find parametric equations for the curve. \(\Rightarrow\)

Sketch the curves over the interval \([0,2 \pi]\) unless otherwise stated. $$ r=\sin \theta+\cos \theta $$

Find an equation in polar coordinates that has the same graph as the given equation in rectangular coordinates. $$ y=\sin x \Rightarrow $$

Find an equation in polar coordinates that has the same graph as the given equation in rectangular coordinates. $$ y=5 x+2 \Rightarrow $$

Find the area inside one loop of \(r=\cos (3 \theta) . \Rightarrow\)