How Accurate is Approximating Sine with Its Series Terms?

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The discussion focuses on approximating the sine function using its infinite series representation. Participants are asked to calculate the forward and backward errors when using only the first term and then the first two terms of the series for specific values of x (0.1, 0.5, and 1.0). The importance of showing work and understanding the calculations is emphasized to facilitate assistance. The conversation encourages engagement by inviting users to share their attempts and challenges. Overall, the thread aims to clarify the accuracy of sine approximations through practical examples.
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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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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.
 

Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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