MHB How Accurate is Lagrange Interpolation for Approximating Cos(0.75)?

AI Thread Summary
The discussion centers on using Lagrange interpolation to approximate cos(0.75) with given cosine values, resulting in an approximation of 0.7313 and an actual error of 0.0004. The error bound calculated is 2.7 × 10^-8, with discrepancies attributed to the precision of the provided data. A user expresses disappointment over a lack of responses to their initial query about the intermediary steps in solving the problem. Other participants encourage sharing the solution for future reference, emphasizing the importance of community support. The conversation highlights the balance between academic integrity and collaborative learning in online forums.
Hero1
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Problem:
Use the Lagrange interpolating polynomial of degree three or less and four digit chopping arithmetic to approximate cos(.750) using the following values. Find an error bound for the approximation.

cos(.6980) = 0.7661
cos(.7330) = 0.7432
cos(.7680) = 0.7193
cos(.8030) = 0.6946

The actual value of cos(.7500) = 0.7317 (to four decimal places). Explain the discrepancy between the actual error and the error bound.

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Solution:
The approximation of cos(.7500) 0.7313. The actual error is 0.0004, and an error bound is 2.7 × 10-8. The discrepancy is due to the fact that the data are given only to four decimal places.

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Can anyone help me figure out the intermediary steps from the problem to solution?
 
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I managed to figure out the solution to the problem myself, however, I am disappointed that no one responded to my thread.
 
Hero said:
I managed to figure out the solution to the problem myself, however, I am disappointed that no one responded to my thread.


Hi Hero,

I'm sorry no one responded to your thread. Over 95% of our threads get responded to, so believe me it's not a normal occurrence. Can you post how you solved the problem for us? Other people in the future might find it useful :)

Jameson
 
Jameson said:
Hi Hero,

I'm sorry no one responded to your thread. Over 95% of our threads get responded to, so believe me it's not a normal occurrence. Can you post how you solved the problem for us? Other people in the future might find it useful :)

Jameson

I can't post it until after the course is over. I don't want my instructor thinking that I stole online content.
 
Hero said:
I can't post it until after the course is over. I don't want my instructor thinking that I stole online content.

You posted the question here hoping someone else would answer it. How is your posting your own work different than someone else posting their work?

I guess if you just won't post your solution, then ok but I don't quite get it. As a rule of thumb I would suggest that you be comfortable with anything you post on this site to be read by anyone.

Again, sorry you didn't get any help but give it one more try and when another question comes up and I'm sure you'll find some help. I'll make sure our staff knows that you have a question if you post next time.
 
Jameson said:
You posted the question here hoping someone else would answer it. How is your posting your own work different than someone else posting their work?

I guess if you just won't post your solution, then ok but I don't quite get it. As a rule of thumb I would suggest that you be comfortable with anything you post on this site to be read by anyone.

Again, sorry you didn't get any help but give it one more try and when another question comes up and I'm sure you'll find some help. I'll make sure our staff knows that you have a question if you post next time.

I will post it
 

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