Approximation sin(x) taylor Series and Accuracy

[engboysclub]

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

Homework Equations

The Attempt at a Solution

I'm not sure how to begin.

 

[mfb]

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%?

 

[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.

 

[engboysclub]

How do i determine the term ?

How do I calculate the accuracy ?

 

[mfb]

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]

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.

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