HIGHLY Rigorous Treatment of the Trigonometric Functions

In summary, Peter is looking for a rigorous treatment of trigonometric functions, including definitions, basic relationships and inequalities, differentiation and integration, and possibly more. He is seeking suggestions for an online resource and a textbook chapter. An offer for tutoring was also made, but Peter is from Hobart, Tasmania and is interested in remote options. A recommendation for free e-books on trigonometry from archive.org was given, as well as a link to a discussion on introducing trigonometric functions in a rigorous analysis course.
  • #1
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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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  • #2
What part of Oz are you from Peter? If Melbourne, I can tutor you...
 
  • #3
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
 
  • #4
Could always be done over Skype though :)
 
  • #5
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
 
  • #6
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

 

FAQ: HIGHLY Rigorous Treatment of the Trigonometric Functions

1. What is the purpose of highly rigorous treatment of trigonometric functions?

The purpose of highly rigorous treatment of trigonometric functions is to provide a mathematical foundation for understanding and analyzing these functions. By rigorously defining and proving the properties of trigonometric functions, we can ensure their validity and accuracy in mathematical applications.

2. What are the key concepts and techniques involved in highly rigorous treatment of trigonometric functions?

The key concepts and techniques involved in highly rigorous treatment of trigonometric functions include the unit circle, right triangle trigonometry, the Pythagorean identity, inverse trigonometric functions, and the complex number system. These concepts are used to prove the properties and relationships of trigonometric functions.

3. How does highly rigorous treatment of trigonometric functions differ from basic trigonometry?

Highly rigorous treatment of trigonometric functions goes beyond basic trigonometry by providing a more formal and rigorous approach to understanding and analyzing these functions. It involves proofs and a deeper understanding of the underlying concepts, rather than simply using formulas and rules.

4. What are some real-world applications of highly rigorous treatment of trigonometric functions?

Highly rigorous treatment of trigonometric functions is applicable in various fields such as physics, engineering, and navigation. It is used to model and solve problems involving periodic motion, waves, and oscillations. It is also used in the calculation of angles and distances in navigation and surveying.

5. How can one improve their understanding of highly rigorous treatment of trigonometric functions?

To improve understanding of highly rigorous treatment of trigonometric functions, one can practice solving various proofs and problems, review the underlying concepts, and seek guidance from a math tutor or instructor. Additionally, studying the history and development of trigonometry can provide a deeper understanding of its foundations and principles.

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