How Accurate is Approximating Sine with Its Series Terms?

[yenbibi]

The sine function is given by the infinite series
sin(x) = x - x³/3! + x⁵/5! + x⁷/7! + ...
a) What are the forward and backward errors if we approximate the sine function
by using only the first term in the series, for x = 0.1, 0.5, 1.0?
b) Using the first two terms.

 

[tiny-tim]

Welcome to PF!

The sine function is given by the infinite series
sin(x) = x - x³/3! + x⁵/5! + x⁷/7! + ...
a) What are the forward and backward errors if we approximate the sine function
by using only the first term in the series, for x = 0.1, 0.5, 1.0?
b) Using the first two terms.

Hi yenbibi! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

 

[HallsofIvy]

Yes, show your work. Looks to me like a simple arithmetic problem.