# Approximation sin(x) taylor Series and Accuracy

## Homework Statement

One uses the approximation sin(x) = x to calculate the oscillation period of a simple gravity pendulum. Which is the maximal angle of deﬂection (in degree) such that this approximation is accurate to a) 10%, b) 1%, c) 0.1%. You can estimate the accuracy by using the next nonvanishing term of the Taylor series

## The Attempt at a Solution

I'm not sure how to begin.

## The Attempt at a Solution

mfb
Mentor
by using the next nonvanishing term of the Taylor series
You could determine this term to begin.

Afterwards: How do sin(x) and x differ if the approximation is accurate to 10%?

I'm not really sure - I know what Taylor series is - Graphically and what it does but I don't know how to implement it or work it out.

How do i determine the term ?

How do I calculate the accuracy ?

mfb
Mentor
Look in your script/book/wikipedia for the taylor series. You cannot solve the problem without any knowledge about taylor series.

How do I calculate the accuracy ?
If the real value is 0.5 and the approximation is 0.45 (arbitrary numbers), what is the relative deviation?

Ray Vickson