The graph of an equation of the form = cos or = sin is a rose, having n leaves if is odd, and 2 leaves if is even. Examples: = 2 cos 4
= 2 sin 4
= 2 cos 5
= 2 sin 5
Other nice results for polar graphs are the following. = , where ≼ 0, (spiral of Archimedes)
= 9 sin 2 (lemniscate)
= 8 (spiral of Fermat)
= csc + 3 (conchoid of Nicomedes)
: = cos + sin 7 + cos 17 , = sin + cos 7 ! + sin 17