Can I Just Use Trigonometric Functions Without Understanding Them?

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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
 
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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.