Can I Just Use Trigonometric Functions Without Understanding Them?

Click For Summary

Discussion Overview

The discussion revolves around the necessity of understanding trigonometric functions for students preparing for exams in mathematics or physics. Participants explore whether it is sufficient to use these functions without a deep comprehension of their underlying principles and implications for future studies.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant questions if it is acceptable to rely on a list of trigonometric functions without fully memorizing them, expressing concern about future implications for a major in math or physics.
  • Another participant emphasizes the importance of knowing trigonometric functions well, suggesting they are frequently applicable in physics and can be crucial for understanding concepts like vectors.
  • A different viewpoint suggests that while not all formulas need to be memorized, a fundamental understanding is necessary to use them effectively and derive other formulas when needed.
  • Specific foundational formulas are mentioned as essential knowledge, indicating that understanding these can facilitate the derivation of more complex trigonometric identities.
  • One participant shares a personal experience, noting that after years of use, they still do not remember all variations of trigonometric formulas but can derive them as needed based on a solid grasp of the basics.

Areas of Agreement / Disagreement

Participants express differing views on the balance between memorization and understanding of trigonometric functions. There is no consensus on whether one can rely solely on memorization or if a deeper understanding is essential.

Contextual Notes

Some participants highlight the importance of foundational knowledge in trigonometry for deriving other formulas, suggesting that reliance on memorization may limit understanding in more complex applications.

Mépris
Messages
847
Reaction score
11
Hi,

For my exams, I am provided with a list of trigonometric functions. I do know at least a good half of those I'm supposed to know but I was wondering if I could get away with *just* knowing how to use them? I know things like sin^2(x)=1 - cos^2(x) or sin(A+B) = sinAcosB + cosAsinB but there are a handful of them I don't remember. Will that be detrimental in the future if I'm majoring in math or physics?

Cheers
 
Mathematics news on Phys.org
It is helpful to know trig as good as you can... You never know when it will come in handy, and it does a LOT especially in physics... I made this little dewhicky to help me when I was learning (still am learning), mostly for vectors in physics. All of the equations come from the original SOH CAH TOA.

Trig.png
 
If you are given a list of formulas, then obviosuly you don't need to remember them all (face-palm!)

On the other hand you do need to understand what they mean, so you can use them sensibly.

FWIW after 30 years using them regularly I still can't remember all the "variations" on trig formulas, but I know enough of them to be able to derive the rest quickly when I need them

If you know the basics of
sin2 a + cos2 a = 1
sin(a+b) = sin a cos b + cos a sin b
cos(a+b) = cos a cos b - sin a sin b
sin(-a) = -sin(a), cos(-a) = cos(a)

You should be able to work out all the other formulas for double and half angles, and
2 sin a cos b = sin(a+b) + sin(a-b) etc.

Then letting a+b = x and a-b = y you can get all the formulas for
(sin or cos a) +/- (sin or cos b).

For complex numbers, everything follows from eix = cos x + i sin x.
 

Similar threads

  • · Replies 28 ·
Replies
28
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 26 ·
Replies
26
Views
4K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K