Math god needed for a trig problem I concted

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Homework Help Overview

The discussion revolves around a trigonometric problem involving the evaluation of nested trigonometric functions and the implications of small angle approximations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the behavior of trigonometric functions for small angles and question the significance of differences in values produced by nested functions. Some suggest looking into the small angle approximation to understand convergence.

Discussion Status

There is an ongoing exploration of the small angle approximation and its effects on the values of nested trigonometric functions. Participants have provided insights and examples, but no consensus has been reached regarding the broader implications or interpretations of the problem.

Contextual Notes

Some participants express concerns about calculator limitations in displaying small differences in values, which may affect the understanding of the problem.

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hw

Delete this, please. I'm stoopid.
 
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That's not particularly special: cos of something is a number between 0 and 1, so you're taking sin of something small (less than 1 degree). So things obviously converge very quickly.
 
Do a search for small angle approximation
 
The above posters hit the nail on the head. In fact, sin(cos(tan(sin(cos(tan(sin(cos(tan(n), is not equal for any integer n. The difference is just so small that your calculator can not display the difference. Thus, the small angle approximation.

Try entering sin(cos(tan(sin(cos(tan(1) and sin(cos(tan(sin(cos(tan(1E10). If your calculator is capable of displaying enough digits, you will find that the approximate value of the first is .017452406437037, while the approximate value of the second is .017452406437039.

If your calculator can't display that many digits, use sin(cos(tan(n) instead.
 

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