Area in Polar Coordinates

Cici2006

1. The problem statement, all variables and given/known data
Find the area of the region bounded by r=8cos10[tex]\Theta[/tex]


2. Relevant equations



3. The attempt at a solution

I set r=0 to find [tex]\Theta[/tex], which i used for my bounds
[tex]\Theta[/tex]=pi/20, 3pi/20
A= [tex]\int[/tex](1/2)64cos^2(10[tex]\Theta[/tex]) d[tex]\Theta[/tex]

TMM

What you need to do is multiply your answer by 20 since you found the area of one of the 20 petals of the rose curve.

Kreizhn

Are you having trouble finding the correct solution since yours is too small? or because you don't know how to evaluate the integral?

If you need help evaluating the integral, use the fact that

[tex] \cos^2{nx} = \frac{1+\cos{2nx}}{2}, n\in\mathbb{N} [/tex]

Cici2006

Okay, let me state what i did in more detail:
A=(1/2)integral 64(cos^2(10theta)) d(theta)
=32 integral (1/2)(1+cos20theta) (theta)
=16[theta-(1/20)sin20theta]
did i do it correct so far?
then i just plug in my bounds which are pi/20 to 3pi/20 right?
now should i just multiply my answer by 20?

Cici2006

thanks for the help i solved it