Apologies if this is poorly formatted - it is my first time posting a question.
I'm trying to find evenly spaced arc lengths along a function (in this case a sinusoid) using the bisection method. However at certain points in the function - when $dy/dx = 0$ - the results I get are not evenly spaced despite getting the right result from the integration (checked in wolfram alpha).
The function I'm evaluating is:
\begin{equation} y = A \sin \left( {2 Pi \over \lambda} x \right) \tag{1} \end{equation}
so the length of an arc on this function is the definite integral of
\begin{equation} \sqrt{1 + (dy/dx)^2} \tag{2} \end{equation}
so to find a set length of arc I use bisection on the definite integral of (2) to find the upper limit corresponding to that length - then feed these back into (1).
I'm using the trapezium method of numerical integration (in a high level language) and the bisection method of root finding. I want the evenly spaced value to be 0.866 in this instance.
As I know what the max value can be I'm setting $a =0$ and $b = 0.866$ for the bisection. So the first guess will be $0.866 / 2$ and so on.
I have included the following images to help illustrate my problem;
note the green part is the place at which i think the problem is...
This is function (2) that is evaluated with numerical integration.
I'm in no way an expert in root finding methods - so perhaps someone who has more experience may see what the problem is or whether the problem may be the numerical method - trapezium method not good enough?
Does any one have a suggestion as to which root finding method may solve this?
Thank you.