91Ó°ÊÓ

Use \((4)\) to parameterize the curve whose polar equation is given. Use a graphing utility to obtain the graph of the resulting set of parametric equations. $$ r=2 \sin \frac{\theta}{4}, \quad 0 \leq \theta \leq 8 \pi $$

Find a polar equation that has the same graph as the given rectangular equation. $$ x^{3}+y^{3}-x y=0 $$

Find a polar equation that has the same graph as the given rectangular equation. $$ x^{2}+y^{2}=5 y $$

The graphs of the equations (a)-(d) represent a rotation of the graph of the given equation. Try sketching these graphs by hand. If you have difficulties, then use a graphing utility. \(r=1+\sin \theta\) (a) \(r=1+\sin (\theta-\pi / 2)\) (b) \(r=1+\sin (\theta+\pi / 2\) (c) \(r=1+\sin (\theta-\pi / 6)\) (d) \(r=1+\sin (\theta+\pi / 4)\)

Use \((4)\) to parameterize the curve whose polar equation is given. Use a graphing utility to obtain the graph of the resulting set of parametric equations. $$ r=2 \cos \frac{\theta}{5}, \quad 0 \leq \theta \leq 5 \pi $$

Use \((4)\) to parameterize the curve whose polar equation is given. Use a graphing utility to obtain the graph of the resulting set of parametric equations. $$ r=2 \cos \frac{3 \theta}{2}, \quad 0 \leq \theta \leq 4 \pi $$

Find a polar equation that has the same graph as the given rectangular equation. $$ 2 x y=5 $$

The graphs of the equations (a)-(d) represent a rotation of the graph of the given equation. Try sketching these graphs by hand. If you have difficulties, then use a graphing utility. \(r=2+4 \cos \theta\) (a) \(r=2+4 \cos (\theta+\pi / 6)\) (b) \(r=2+4 \cos (\theta-3 \pi / 2)\) (c) \(r=2+4 \cos (\theta+\pi)\) (d) \(r=2+4 \cos (\theta-\pi / 8)\)

Find a rectangular equation that has the same graph as the given polar equation. $$ r=2 \sec \theta $$

Use a CAS to obtain graphs of the polar equation \(r=a+\cos \theta\) for \(a=0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \ldots, 3\).