how do you find the points of intersection algebraicly?
1-cos(theta) = 1+cos(theta)
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
Hello, jeph!
I assume these are polar curves (two cardioids).Find the points of intersection: .1 + cosθ .= .1 - cosθ
. . Jhevon was absolutely correct.
We have: .2·cosθ = 0 . → . cosθ = 0 . → . θ = ±½π
The points of intersection are: .(1, ½π), (1, -½π)
Hello, Jhevon!
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.