Pendulum Oscillation Frequency?

[DivideBy0]

Homework Statement

Given a pendulum with fixed length, at what angle does the pendulum have to be released at in order to not follow the standard formula for frequency?

Homework Equations

P = 2pi*sqrt(l/g)

The Attempt at a Solution

I know that this equation holds for "small" angles (theta < 15 degrees?), but at what angle does this break? And why does it not work only after a specific angle?

 

[ehild]

The formula is never true exactly, it is an approximation. Up to what angles you can use it, depends how accurately you need the period. From the Taylor expansion of sin(theta) you can estimate the interval of validity.