directions - write the equation for each of the following polar rose graphs. mrs. bernacki - sju pre…

Explanation:

Step1: Recall polar - rose equation form

The general form of a polar - rose curve is $r = a\cos(n\theta)$ or $r = a\sin(n\theta)$. If $n$ is odd, the number of petals is $n$. If $n$ is even, the number of petals is $2n$.

Step2: Analyze graph 1

The graph has 8 petals. Since the number of petals is even, using the formula for the polar - rose curve $r = a\cos(n\theta)$ or $r = a\sin(n\theta)$ with $2n = 8$, we get $n = 4$. Let's assume $a = 2$ (the amplitude can be adjusted based on the size of the petals). A possible equation is $r = 2\cos(4\theta)$.

Step3: Analyze graph 2

The graph has 4 petals. Since the number of petals is even, with $2n=4$, we have $n = 2$. A possible equation is $r = 2\sin(2\theta)$.

Step4: Analyze graph 3

The graph has 5 petals. Since the number of petals is odd, $n = 5$. A possible equation is $r=- 2\cos(5\theta)$ (the negative sign can change the orientation).

Step5: Analyze graph 4

The graph has 4 petals. Since the number of petals is even, with $2n = 4$, we have $n = 2$. A possible equation is $r = 2\cos(2\theta)$.

Step6: Analyze graph 5

The graph has 4 petals. Since the number of petals is even, with $2n = 4$, we have $n = 2$. A possible equation is $r = 3\sin(2\theta)$ (the value of $a$ is chosen based on petal - size).

Step7: Analyze graph 6

The graph has 4 petals. Since the number of petals is even, with $2n = 4$, we have $n = 2$. A possible equation is $r = 2\cos(2\theta)$.

Answer:

1. $r = 2\cos(4\theta)$
2. $r = 2\sin(2\theta)$
3. $r=-2\cos(5\theta)$
4. $r = 2\cos(2\theta)$
5. $r = 3\sin(2\theta)$
6. $r = 2\cos(2\theta)$