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
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.
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 sin^{2} a + cos^{2} 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.