- #1

ChickysPusss

- 13

- 1

## Homework Statement

OK, I need to solve for the fixed point of the equation

2sinπx + x = 0

on the interval [1, 2]. I know the answer to be ~1.21... but I need to prove it.

## The Attempt at a Solution

I really just need help solving for a proper equation of x. I tried x = -2sinπx, but that doesn't work on the interval for the method I am using to solve for the fixed point (Banach).

So I tried this

2sinπx = -x

sinπx = (-x/2)

πx = arcsin(-x/2)

x = (1/π)*arcsin(-x/2)

But this equation seems totally wrong, as anything past 0 is negative. Can anyone tell me what I'm doing wrong, or perhaps that there is another way to solve for x? Thanks.