Error Analysis of Sin(x) with x=2±0.2

[zak8000]

Homework Statement

let x=2±0.2
y=sin(x)

write y in the form mean±error

i don't know how to perform error analysis on the sine function help please

Homework Equations

The Attempt at a Solution

i looked through a physics textbook and saw something which might help me

$$(sigma)$$^2=$$d^2f/dx^2$$*$$\sigma1^2$$

 

[I like Serena]

The proper formula is that when you have :

x ± Δx,
where Δx is the standard deviation of the measurement x

and y = f(x)

then the standard deviation Δy for given x ± Δx is:

Δy = |f'(x)| Δx

Can you apply that to your problem?