Solving Iterative Method Homework | Physics Problem Help

[maherelharake]

Homework Statement

I have a physics problem, but the math part is where I am getting stuck. I have to use the iterative method, which I understand, but I can't seem to get the correct result. My problem is that I have to plug the value of x=1.9195 into an equation f₁(x)=(x/10)(x+3). I get a value of 0.9443 for f₁(x). I then take that f₁(x) and plug it into x=arcsin(f₁(x). I am supposed to get something close to 1.9 for the new 'x' but when I do this, I get 1.2. This is strange to me because the sin of 1.9195 is 0.94 but the arcsin of 0.94 is 1.22 instead of 1.9195. Can anyone clear this up for me?

Homework Equations

The Attempt at a Solution

 

[Dick]

arcsin(sin(x))=x is only true for x in the range [-pi/2,pi/2]. Do you see why? 1.9195 is outside of that range. 1.22~pi-1.9195. Draw a graph of sin and arcsin.

 

[maherelharake]

Ohh ok that makes sense now. Well I am not sure how to proceed with this problem then. Do you have any ideas? I have a function f₁(x)=(x/10)(x+3) and f₂(x)=sin(x). These two functions of x are equal. I have an initial x value of 1.9195. I am supposed to take this value and plug it into f₁(x) and use that result and plug it into x=arcsin(f₂(x)). I am supposed to have a convergence on the number x=1.9151. Any ideas on how to do this since this way doesn't seem to work? Thanks again.