trigonometry
I'm trying to find the points where (y = 2 sin x) and (x = 2 sin y) intersect, besides (0, 0).
I've managed to work out that 2 sin x should equal x.
My classpad can give me an answer that I believe is right, simply by looking at these two sine functions on a graph. But how can I go about solving this problem?
Thanks in advance.
Ok, I have found how to fit my sine curve. I have done it by adding delta y between those two vectors into the value of found sine function (blue). However, the sine wave which is now fitted between points is a little bit different (violet). I got a question for all you experts, does it affect the length of sine wave which i found or the length of the original and "moved" curves are the same? Here is the image
Best Answer
plugging $$x=2\sin(y)$$ into your first equation you will get $$y=2\sin(2\sin(y))$$ this equation can only be solved by a numerical way,e.g. the Newton-Raphson method. one solution is given by $$1.895494267$$