Looking for a good book about trigonometry

In summary: Explanation is somehow terse. But problems are good. He divides them to exercises & problems. exercises are almost straightforward questions but problems make you think. In general, I would consider axler books between dry & rigorous levels. I took cohen as main book & axler as supplementary for problems. Was very rewarding combination.
  • #1
Theia
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Hi all!

I've never been studied the identities and such of secant, cosecant and cotangent. Yet I think, it would be useful to have them in my toolbox. Thus I'm asking, if anyone would know a reasonable book or other kind of material (paper or pdf) about trigonometry that has brief theory section with examples and fairly lot of exercises.

As for language preference, I prefer English, but maybe can manage to read some other language too as math is universal.
 
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Phase 1 (Gentle introduction) : Trigonometry by Lial. (Know concept in general without any in-depth explanation, easy problems to get used with subject + has good geometry refresher in first chapter).
Phase 2 (Better problem set) : Trigonometry chapters in precalculus by david cohen. Much better problem sets, most of explanation you already covered in Lial book. Up to this phase you are absolutely fine with trigonometry.
Phase 3 (In-depth explanation) : Plane trigonometry by SL Loney. Famous book. Using geometry to prove almost everything. This is book is from 19th century & still used in some countries like India. Explain every thing in-depth. Fully solved by many indian teachers in youtube/ pdf. Requires good geometry background.
Phase 4 (More in-depth) : A treatise on plane trigonometry by Hobson. Ok, this is higher one, requires solid geometry background. More challenging exercises. You will be trig master.

Problem books :
1- Solutions to SL Loney trigonometry. (Already mentioned).
2- Problems in trigonometry by todhunter.

Bottom line : Phase 2 is more than enough for most students. If you want only one book, go with trig chapters in david cohen precalculus book.
 
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  • #5
MiddleEast said:
Phase 1 (Gentle introduction) : Trigonometry by Lial. (Know concept in general without any in-depth explanation, easy problems to get used with subject + has good geometry refresher in first chapter).
Phase 2 (Better problem set) : Trigonometry chapters in precalculus by david cohen. Much better problem sets, most of explanation you already covered in Lial book. Up to this phase you are absolutely fine with trigonometry.
Phase 3 (In-depth explanation) : Plane trigonometry by SL Loney. Famous book. Using geometry to prove almost everything. This is book is from 19th century & still used in some countries like India. Explain every thing in-depth. Fully solved by many indian teachers in youtube/ pdf. Requires good geometry background.
Phase 4 (More in-depth) : A treatise on plane trigonometry by Hobson. Ok, this is higher one, requires solid geometry background. More challenging exercises. You will be trig master.

Problem books :
1- Solutions to SL Loney trigonometry. (Already mentioned).
2- Problems in trigonometry by todhunter.

Bottom line : Phase 2 is more than enough for most students. If you want only one book, go with trig chapters in david cohen precalculus book.
Just curious, have you read Axler's precalculus text? I wonder how his problems compare
 
  • #6
Muu9 said:
Just curious, have you read Axler's precalculus text? I wonder how his problems compare
I did not like the trig section., particularly the section of graphing said functions. ie., period /phase shifts.
 
  • #7
Muu9 said:
Just curious, have you read Axler's precalculus text? I wonder how his problems compare
Explanation is somehow terse. But problems are good. He divides them to exercises & problems. exercises are almost straightforward questions but problems make you think. In general, I would consider axler books between dry & rigorous levels. I took cohen as main book & axler as supplementary for problems. Was very rewarding combination.
 

1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles.

2. Why is it important to learn trigonometry?

Trigonometry is used in various fields such as engineering, physics, and navigation. It is also a fundamental concept in calculus and other advanced math courses.

3. What are some real-world applications of trigonometry?

Trigonometry is used in architecture to calculate the dimensions of buildings and in surveying to measure land. It is also used in astronomy to calculate distances between celestial objects.

4. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions relate the angles of a triangle to the lengths of its sides.

5. How can I improve my understanding of trigonometry?

Practice is key to understanding trigonometry. You can also use online resources, textbooks, and seek help from a tutor or teacher if needed.

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