Chapter 6.3, Problem 3PS

(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: $r^2=9\cos 2\theta$ .

(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: $r=2\sin \left(\frac{\pi }{6}\right)$ .

(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: $r=3\sin \left(3\theta \right)$ .

(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: $r=3\theta$ .

(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: $r=2-2\cos \theta$ .

(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: $\theta =\frac{\pi }{6}$ .

(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: $r^2=\sin 2\theta$ .

(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: $r-2=4\cos \theta$ .