Question
Rose curves are characterized by equations of the form $r=a \cos (n \theta)$ or $r=a \sin (n \theta), a \neq 0$. If $n \neq 0$ is even, the rose has_____ petals; if $n \neq \pm 1$ is odd, the rose has petals.
Step 1
If $n \neq 0$ is even, the rose has $n$ petals. This is because for even values of $n$, the cosine and sine functions complete $n/2$ full periods in the interval $0 \leq \theta \leq 2\pi$, resulting in $n$ petals. Show more…
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Rose curves are characterized by equations of the form $r=a \cos (n \theta)$ or $r=a \sin (n \theta), a \neq 0 .$ If $n \neq 0$ is even, the rose has ___________ petals; if $n \neq \pm 1$ is odd, the rose has ___________ petals.
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Rose curves are characterized by equations of the form $r=a \cos (n \theta)$ or $r=a \sin (n \theta), a \neq 0 .$ If $n \neq 0$ is even, the rose has _____ petals. petals; if $n \neq \pm 1$ is odd, the rose has_____ petals.
THINK ABOUT IT How many petals do the rose curves given by $r=2\ \cos\ 4\theta$ and $r=2\ \sin\ 3\theta$ have? Determine the numbers of petals for the curves given by $r=2\ \cos\ n\theta$ and $r=2\ \sin\ n\theta$, where $n$ is a positive integer.
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