thanx for all help!
use mclaurin series to compute the sin 3 degrees, correct to 5 decimal places.
use taylos inequality to show you are within 5 decimal places.
i found the bound for the sinx, its obviously one but i dont know wat that means or how to set it up.
please help!
thanx!
The McLaurin series is
It is well known that the Mclaurin series of sinx leads to...
I'm assuming your questions says evaluate until we get to the third power (not entirely clear from your post) so what you're looking for is
But to be honest, your question is too unclear for me to get to any sort of answer here. What are you looking for?
Taylor's inequality says that the error in approximating the infinite series (Taylor's series) by truncating at the Nth power is less than where M is an upper bound on the absolute value of the Mth dervivative of f between x and .
All derivatives of sin(x) are or both of which have maximum value over all x of 1, as you say. Of course, the derivative of sin(x) is cos(x) and the derivative or cos(x) is -sin(x) only when x is measured in radians so and , approximately.
So the errror is less than and you want to make that .00001.
I would recommend just evaluating that at N= 3, 4, 5, ... until it gets small enough.