Aproximation arccos(1/4)

1. Jan 25, 2009

namehere

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

2. Jan 25, 2009

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.

3. Jan 25, 2009

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.