Rose line of polar coordinates (polar coordinates? Rose) is a very famous curve in mathematics, which looks like a petal. Can only be described by polar coordinate equation, the equation is as follows:

r(θ)？ =? a*cos？ kθ？ or

r(θ)？ =? Answer? Sin? kθ，

If k is an integer, then when k is odd, the curve will be k petals, and when k is even, the curve will be 2k petals. If k is non-integer, a disc-shaped figure will be generated, and the number of petals is also non-integer. Note: this equation cannot produce a multiple of 4 plus 2 petals (for example, 2,6, 10 ...). The variable A represents the length of rose petals. ?

What is the equation? r(θ)？ =? 2? Sin? 4θ rose line: