Advanced study of trigonometry

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Discussion Overview

The discussion centers around the advanced study of trigonometry, particularly in the context of preparing for a mathematics degree and its relevance in higher mathematics courses such as calculus. Participants explore the depth and application of trigonometry beyond precalculus.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant inquires about the extent of trigonometry in higher mathematics and whether it is revisited after precalculus.
  • Another participant suggests that trigonometry does not significantly expand beyond precalculus, mentioning the sine law and cosine law as potentially the most advanced topics.
  • A later reply emphasizes that trigonometric functions, particularly sine and cosine, are important due to their periodic nature, rather than solely for solving triangles.
  • Another participant notes that college-level courses may cover trigonometry in more depth, including topics like vectors and exponential forms, which may be revisited in calculus courses.

Areas of Agreement / Disagreement

Participants express varying views on the depth of trigonometry in higher mathematics, with some suggesting it remains relatively basic while others indicate that college courses may provide a more thorough exploration.

Contextual Notes

There is mention of potential confusion regarding course names and content, as well as the use of voice recognition technology leading to errors in communication.

dmehling
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I was just wondering if anyone could suggest information about the advanced study of trigonometry. I am contemplating getting a degree in mathematics, and I'm currently trying to master the basics of trigonometry in preparation for taking cactus. In looking at all the courses I'll be taking for an undergraduate degree in mathematics, I don't see any mention of trigonometry. Is that something that shows up again in higher mathematics, or is what I have learned in precalculus about all there is to trigonometry?
 
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First, I hope you are planning on taking "Calculus". If you really are planning on taking "cactus", remember to wear heavy gloves!

Trigonometry itself really does not include a great deal more than you learn in precalculus. I suspect that the sine law and cosine law, for solving general triangles are about as "advanced" as trigonometry gets. However, the trigonometric functions, especially sine and cosine, are heavily used- not so much to solve problems dealing with triangles, but because they are the simplest periodic functions.
 
Thanks for the information. Yes I definitely will be taking calculus. I had no idea I said cactus. I use voice recognition to type so sometimes I end up with errors like that.
 
Keep looking. You should find that the first three and least advanced college level Math courses are Trigonometry, College Algebra, and PreCalculus(also called Elementary Functions; also called College Algebra And Trigonometry). The Trigonometry course from college, if it was not in high school, may be a bit more thorough than what you were used to. You might think of this as more advanced. In the college course, you will study vectors and an exponential form of expressing functions and vectors, something which is more thoroughly developed in your Calculus 2 course which you would take LATER.
 

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