HIGHLY Rigorous Treatment of the Trigonometric Functions

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Discussion Overview

The discussion centers around seeking a highly rigorous treatment of trigonometric functions, covering their definitions, relationships, inequalities, differentiation, and integration. Participants are looking for both online resources and textbook recommendations.

Discussion Character

  • Exploratory
  • Homework-related

Main Points Raised

  • Peter expresses a desire for a rigorous treatment of trigonometric functions and requests suggestions for online resources and textbook chapters.
  • Several participants offer to assist Peter, including a tutoring offer from a participant in Melbourne.
  • One participant suggests archive.org as a resource for free e-books on trigonometry.
  • Peter mentions finding an interesting discussion on Math Stack Exchange regarding the introduction of trigonometric functions in a rigorous analysis course.

Areas of Agreement / Disagreement

The discussion does not present any consensus, as participants are sharing resources and offers of help without resolving the initial request for a rigorous treatment.

Contextual Notes

Participants have not specified particular definitions or frameworks for "rigorous" treatment, leaving the interpretation open. The discussion includes various suggestions without evaluating their suitability or rigor.

Who May Find This Useful

Individuals seeking rigorous mathematical treatments of trigonometric functions, educators looking for teaching resources, and students in need of comprehensive study materials.

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I am looking for a rigorous (preferably HIGHLY rigorous) treatment of the trigonometric functions from their definitions through to basic relationships and inequalities through to their differentiation and integration ... and perhaps further ...

Can someone please suggest

(i) an online resource for this ...

(ii) a textbook chapter ...

Peter
 
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What part of Oz are you from Peter? If Melbourne, I can tutor you...
 
Prove It said:
What part of Oz are you from Peter? If Melbourne, I can tutor you...
Hi Prove It,

I am from Hobart, Tasmania

Thanks for the kind offer though ...

Peter
 
Could always be done over Skype though :)
 
Peter said:
I am looking for a rigorous (preferably HIGHLY rigorous) treatment of the trigonometric functions from their definitions through to basic relationships and inequalities through to their differentiation and integration ... and perhaps further ...

Can someone please suggest

(i) an online resource for this ...

(ii) a textbook chapter ...

Peter
Hi Peter,
A good resource for free e-books if archive.org. For books on trig, you could look at
https://archive.org/search.php?query=trigonometry
 
John Harris said:
Hi Peter,
A good resource for free e-books if archive.org. For books on trig, you could look at
https://archive.org/search.php?query=trigonometry
Thanks for the help, John ... ...

I also found an interesting discussion of

[h=1]The best way to introduce trigonometric functions in a rigorous analysis course
[/h]at Math Stack Exchange ... ...

See

undergraduate education - The best way to introduce trigonometric functions in a rigorous analysis course - Mathematics Educators Stack ExchangePeter

 

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