How Much is Trig Used in Maths Outside of Calculus?

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Discussion Overview

The discussion centers on the role and prevalence of trigonometry in mathematics beyond calculus, exploring its applications in various mathematical fields and the personal experiences of participants with the subject.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses a lack of enthusiasm for trigonometry and questions its necessity in other areas of mathematics.
  • Another participant notes that trigonometry is heavily used in differential equations and vector calculus, while its use in linear algebra is limited to specific topics like transformations.
  • A claim is made that trigonometry is the most important pre-calculus topic, indicating its foundational role in further mathematical studies.
  • Some participants argue that a dislike for trigonometry may stem from a lack of understanding or poor teaching experiences, emphasizing its beauty and importance in mathematics and science.
  • Trigonometry is described as being essential not only in mathematics but also in fields like optics, highlighting its broad applicability.
  • A participant reflects on their regret for not memorizing trigonometric identities, suggesting that familiarity with the subject can ease problem-solving in various contexts.
  • There is a distinction made between the geometric aspects of trigonometry and its application in periodic functions, with the latter being more prevalent in certain mathematical problems.

Areas of Agreement / Disagreement

Participants express a range of opinions about trigonometry, with some valuing its importance and others sharing negative experiences. There is no consensus on the extent of its necessity or the reasons for disliking the subject.

Contextual Notes

Some participants mention personal experiences and educational backgrounds that may influence their views on trigonometry, but these perspectives are not universally applicable.

SF49erfan
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My trig. is so-so (I honestly hated it) and just curious how much it's used and needed in other maths? Thanks.
 
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As an Undergrad, here are the math courses I've taken:

Diff EQ - Used trig nonstop
Linear Algebra - not much trig, only once we got to transforms (rotations)
Vector Cal - lots of trig
 
It is used and needed a lot. Of all the pre-calculus topics, trig is the most important one.
 
SF49erfan said:
I honestly hated it
You really need to change that.
 
Somebody who hates trig either:
1) Didn't understand it
2) Had a bad teacher/class
Trigonometry is one of the most beautiful subjects of mathematics and science. It's a very ancient piece of mathematics, but very important. I think I'd like to call it one of the major achievements of scientists. Seriously, if you see everything you can do with trig and all the application it has, it is hard not to be impressed.
 
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Very much both IN mathematics and in other fields which rely on mathematics. Optics is one part of science and technology in which Trigonometry is extensively in action.

What a student really hates is restricted time in which to earn a grade, and the effort to relearn and maintain the concepts and skills while trying to learn more... also for a grade under another time constraint.
 
SF49erfan said:
My trig. is so-so (I honestly hated it) and just curious how much it's used and needed in other maths? Thanks.

Should make it a habit to get good at the things you enjoy least, both in the workplace and in adademia.
 
I didn't LIKE trig but it's certainly useful. I really wish I'd just memorized all the identities back in high school (/taken IB HL maths instead of goddamned maths studies) so I wouldn't have to stop and look them up every 5 seconds.

Anyway, it's ubiquitous. Same as algebra, it's just a fundamental thing that comes up constantly, you don't really think of it as "trigonometry" as a separate subject or thing, it's just part of solving various problems. Plus most of the time it makes things easier to solve anyway if they're based off periodic functions and stuff, or to represent complex things in the trig form (forget what it's actually called).

That said, how much of it is triangles vs periodic functions varies. Generally it's not so much the geometric stuff as it is the functions that crop up constantly (although sometimes the former does show up depending on the problems).
 

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