Solution:
1) Rose:
Rose curve equations have two forms: r = a cos(nθ) and r = a sin(nθ) where a ≠ 0 and n is a positive integers. Petals have length determined by a. If n is odd, the number of petals is n. However, if n is even, the number of petals is 2n.
The equation of a rose has two forms which are
[tex]\begin{gathered} r=a\cos(n\theta) \\ r=asin(n\theta) \end{gathered}[/tex]
The graph of a polar rose is given below as
2)Limacon:
The polar equation is in the form of a limaçon, r = a – b cos θ. Since the equation passes the test for symmetry to the polar axis, we only need to evaluate the equation over the interval [0, π] and then reflect the graph about the polar axis.
[tex]=a-bcos\theta[/tex]
3)A circle:
