Area enclosed by one petal of the rose ?

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In summary, The problem involves finding the area enclosed by one petal of a rose with the equation r=6cos3\theta. To solve the problem, the "half angle" formulas can be used to find the integral, with the integration limits being \theta = \frac{\pi}{3} and \theta = \pi. The first petal is bounded by these two points where cos(3\theta)=0.
  • #1
hamburgler
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I would appreciate any help on this problem because I am completely confused. :confused:

1. The problem statement...

What is the area enclosed by one petal of the rose r=6cos3[tex]\theta[/tex]?
(w/o a calc)2. The sorry attempt...

(1/2)[tex]\int[/tex](6cos3[tex]\theta[/tex])^2d[tex]\theta[/tex]

and the integral is from [tex]\pi[/tex] to [tex]\pi[/tex]/3

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

So then [tex]\int[/tex](6cos3[tex]\theta[/tex])^2d[tex]\theta[/tex]

and then I get stuck at the integral of the function...
 
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  • #2
You can use the so-called "half angle" formulas to find the integral: [itex]cos(\frac{\theta}{2})= \sqrt{\frac{cos(\theta)+1}{2}}[/itex]. 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 [itex]\theta > 0[/itex] where [itex]cos(3\theta)=0[/itex]
 
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What is the area of one petal of a rose?

The area of one petal of a rose can vary depending on the size and type of the rose. However, on average, the area is between 2-5 square inches.

How is the area of one petal of a rose calculated?

The area of a petal can be calculated using the formula for the area of an ellipse, as a rose petal has an elliptical shape. The formula is A = π * a * b, where a and b are the lengths of the semi-major and semi-minor axes, respectively.

Can the area of a rose petal change?

Yes, the area of a rose petal can change as the petal grows and expands. The area can also be affected by external factors such as weather and soil conditions.

Is the area of a rose petal the same for all types of roses?

No, the area of a rose petal can vary depending on the type of rose. Different types of roses can have varying petal sizes and shapes, resulting in different areas for each petal.

Why is the area of a rose petal important to study?

The study of the area of a rose petal can provide insight into the growth and development of roses. It can also be used in breeding and cultivation to produce roses with desired petal sizes and shapes.

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