Chapter 6.3, Problem 4PS

(a)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $r=2\sin 2\theta$ .

(b)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $r^2=2\cos 2\theta$ .

(c)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $r=5\cos {60}^{\circ }$ .

(d)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $r=5\sin 8\theta$ .

(e)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $r\theta =3$ .

(f)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $r^2=9\cos \left(2\theta -\frac{\pi }{4}\right)$ .

(g)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $r=\sin 3\left(\theta +\frac{\pi }{6}\right)$ .

(h)

To determine

To identify: the given curve as a cardioid, rose curve (state number of petals), lemniscate, limacon, circle, line, or none of the above: $\cos \theta =1-r$ .