Can I Just Use Trigonometric Functions Without Understanding Them?

[Mépris]

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

 

[stallionx]

https://www.physicsforums.com/showthread.php?t=526880


I hope this link helps

 

[Allenman]

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.

 

[AlephZero]

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 e^ix = cos x + i sin x.

 

[CellCoree]

,

I can assure you that having a good understanding of trigonometric functions is crucial for success in math and physics. While memorizing specific equations and identities is important, it is equally important to understand the fundamental concepts behind these functions. This will not only help you in solving problems, but also in understanding their applications in various fields of science.

Furthermore, as you progress in your studies, you will encounter more complex trigonometric functions and their applications. It is important to have a strong foundation in these basic functions in order to build upon them and tackle more advanced concepts. So while it may seem tempting to just focus on knowing how to use the functions, it is important to also have a solid understanding of their properties and relationships.

In summary, having a thorough understanding of trigonometric functions is essential for success in math and physics. While memorizing specific equations can be helpful, it is important to also focus on understanding the underlying concepts. This will serve you well in the future as you continue to study and apply these functions in your scientific pursuits. Good luck with your exams!