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

[Hero1]

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?

 

[Hero1]

I managed to figure out the solution to the problem myself, however, I am disappointed that no one responded to my thread.

 

[Jameson]

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

 

[Hero1]

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.

 

[Jameson]

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.

 

[Hero1]

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