# Area enclosed by one petal of the rose ?

1. Mar 24, 2008

### hamburgler

I would appreciate any help on this problem because I am completely confused.

1. The problem statement...

What is the area enclosed by one petal of the rose r=6cos3$$\theta$$?
(w/o a calc)

2. The sorry attempt...

(1/2)$$\int$$(6cos3$$\theta$$)^2d$$\theta$$

and the integral is from $$\pi$$ to $$\pi$$/3

I'm pretty sure that's how you set it up, but I saw other people doing it another way.

So then $$\int$$(6cos3$$\theta$$)^2d$$\theta$$

and then I get stuck at the integral of the function...

Last edited: Mar 24, 2008
2. Mar 24, 2008

### jhicks

You can use the so-called "half angle" formulas to find the integral: $cos(\frac{\theta}{2})= \sqrt{\frac{cos(\theta)+1}{2}}$. Just from what I figure the graph looks like, your integration limits are wrong also. The first petal will be bounded by the first two times for $\theta > 0$ where $cos(3\theta)=0$

Last edited: Mar 24, 2008