How to Approximate arccos(1/4) by Hand?

[namehere]

how to aproximate arccos(1/4) by hand?

 

[king vitamin]

Well the Taylor Series for arccos(x) begins as pi/2 - x - x^3/6, since (1/4)^3/6 = .003 this is a pretty good approximation:

arccos(1/4) \approx \pi/2 - x - x^{3}/3 \approx 1.318

knowing that pi/2 is about 1.57 might help too.

 

[scorpion990]

The derivative of f(x) = arccos(x) can be written as a power series (a binomial series). Find this series, integrate both sides, check for convergence, and plug in x = 1/4.