Question

Rose curves are characterized by equations of the form$r=a\cos \left(n\theta \right)orr=a\sin \left(n\theta \right),a\ne 0.$If $n\ne 0$is even, the rose has _____ petals; if $n\ne \pm 1$is odd, the rose has ______ petals.

Short answer

Rose curves are characterized by equations of the form $r=a\cos \left(n\theta \right)orr=a\sin \left(n\theta \right),a\ne 0.$If $n\ne 0$ is even, the rose has$2n$petals; if$n\ne \pm 1$is odd, the rose has$n$petals.

Step-by-step solution

Step 1. Given Information

The given equation is of rose curves $r=a\cos \left(n\theta \right)orr=a\sin \left(n\theta \right),a\ne 0$

We have to find the rose petals if $n\ne 0$is even and$n\ne \pm 1$, is odd.

Step 2. Filling the blank 

If $n\ne 0$, is even, the rose has 2npetals.

If$n\ne \pm 1$is odd, the rose hasnpetals.