mycroft holmes
Last Activity: 11 Years ago
as a first approximation you could use a few terms from the taylor expansion of cos x.
So, x = 1 - x^2/2 gives us x = 0.73 which is close to the solution x = 0.7391
In fact, if you take a calculator take say x =1 and keep punching the cos key, you will arrive at this number (after around 80 steps max to get the accurate answer)
To know why this process works see Banach Fixed Point Theorem.