# Approximation sin(x) taylor Series and Accuracy

1. Nov 27, 2012

### engboysclub

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

I'm not sure how to begin.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 27, 2012

### Staff: Mentor

You could determine this term to begin.

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

3. Nov 27, 2012

### engboysclub

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.

4. Nov 27, 2012

### engboysclub

How do i determine the term ?

How do I calculate the accuracy ?

5. Nov 27, 2012

### Staff: Mentor

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

If the real value is 0.5 and the approximation is 0.45 (arbitrary numbers), what is the relative deviation?

6. Nov 27, 2012

### Ray Vickson

The thing to do is just to START: write down the Taylor expansion for sin(x). Stop agonizing over it, and just use what you have been taught; that will get you part way towards the solution. Then, if you are stuck at a later stage, you can ask a more pointed and more meaningful question.

RGV