Question

Sketch two circles: r1 = 2 cos θ and r2 = sin θ
and calculate the area of the region that is covered by both of the circles.

Answer 1

im assuming your doing this by polar coordinates?

Answer 2

Of course, I can sketch it, but I cannot find the area.

Answer 3

It's just the second circle, right?

Answer 4

do you mind drawing the polar coordinates from me then i will solve it for you afterwards

Answer 5

http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+sin%28theta%29%2C+r+%3D+2+cos+theta

you meant to find the area betwen the two circles or of each individual circle??

Answer 6

the area between the two circles.

Answer 7

This is what I'm looking for.

Answer 8

for that ... i suggest you change the it into Cartesian coordinate

solve these r1 = 2 cos θ and r2 = sin θ
2 cos θ = sin θ, θ = arctan 2

area = \( \int_{0}^{\theta} r_1^2d\theta + \int_{\theta}^{\pi/2}r_2^2d\theta \) (i hope there will be some other methods)

Answer 9

ok so we know the formula is A=integral of 1/2r^2dtheta from a to b in this case A=1/2integral of (2cost - sint) from 0 to arctan 2

Answer 10

sorry i forgot to square it