How Accurate is Approximating Sine with Its Series Terms?

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SUMMARY

The discussion focuses on the approximation of the sine function using its Taylor series expansion, specifically analyzing the forward and backward errors when using the first and second terms of the series for values x = 0.1, 0.5, and 1.0. The sine function is expressed as sin(x) = x - x³/3! + x⁵/5! + x⁷/7! + ... The participants emphasize the importance of showing work to identify where assistance is needed, indicating that the problem is fundamentally arithmetic in nature.

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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.
 
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Welcome to PF!

yenbibi said:
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! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
Yes, show your work. Looks to me like a simple arithmetic problem.
 

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