# find intersetion points

• Apr 8th 2007, 12:00 PM
jeph
find intersetion points
how do you find the points of intersection algebraicly?
1-cos(theta) = 1+cos(theta)
• Apr 8th 2007, 12:06 PM
Jhevon
Quote:

Originally Posted by jeph
how do you find the points of intersection algebraicly?
1-cos(theta) = 1+cos(theta)

let theta be x

1 - cos(x) = 1 + cos(x)
=> 1 = 1 + 2cos(x) ............added cos(x) to both sides
=> 0 = 2cos(x) .................subtracted 1 form both sides.

so we want all x's such that

2cos(x) = 0
=> cos(x) = 0
=> x = cos^-1(0)
=> x = pi/2 + k*pi
• Apr 8th 2007, 01:01 PM
jeph
dont the curves intersect at 0 also? do i need to plug in the pi/2 into just 1 of the equations to find the intersection?
• Apr 8th 2007, 01:09 PM
Jhevon
Quote:

Originally Posted by jeph
dont the curves intersect at 0 also? do i need to plug in the pi/2 into just 1 of the equations to find the intersection?

the curves DO NOT intersect at 0

remember cos(0) is 1

so 1 - cos(0) = 1 - 1 = 0

and 1 + cos(0) = 1 + 1 = 2

so 1 - cos(x) is not equal to 1 + cos(x) at x = 0

no, pluging in is not necessary, the intersection points are the values of x (which is what i called theta) i gave you.

below is a graph that show some of the intersections

the graph intersects for pi/2 and every multiple of pi before and after that
• Apr 8th 2007, 01:12 PM
Soroban
Hello, jeph!

Quote:

Find the points of intersection: .1 + cosθ .= .1 - cosθ
I assume these are polar curves (two cardioids).
. . Jhevon was absolutely correct.

We have: .2·cosθ = 0 . . cosθ = 0 . . θ = ±½π

The points of intersection are: .(1, ½π), (1, -½π)

• Apr 8th 2007, 01:16 PM
Jhevon
Quote:

Originally Posted by Soroban
Hello, jeph!

I assume these are polar curves (two cardioids).
. . Jhevon was absolutely correct.

We have: .2·cosθ = 0 . . cosθ = 0 . . θ = ±½π

The points of intersection are: .(1, ½π), (1, -½π)

is there any particular reason you assumed they were polar curves, Soroban?
• Apr 8th 2007, 05:36 PM
Soroban
Hello, Jhevon!

Quote:

is there any particular reason you assumed they were polar curves, Soroban?

Well, just their appearance, especially the use of θ (theta).

It suggested an "Area between two polar curves" problem . . .
In this case: .r .= .1 + cosθ .and .r .= .1 - cosθ
. . and theor intersections (polar coordinates) must be determined.