Question

Soft question: How did YOU memorize all those trig identities?

Answer 1

I have trouble memorizing trig identities.

Please don't tell how they SHOULD be memorized, but please tell how YOU memorized them.

Answer 2

\[e^{i \theta}=\cos(\theta)+\sqrt{-1} \sin(\theta)\]

Answer 3

Of course I know the basics, my dear sir. :P
I have trouble memorizing double-angle and half-angle identities for trig functions.

Answer 4

@henpen: Please don't entertain me with Euler's Formula. :P

Answer 5

It makes it so much easier, though!

Answer 6

How so?

Answer 7

(Excited)

Answer 8

Just play with it.

Answer 9

@nincompoop: lol come on.

Answer 10

\[e^{i2x}=(e^{ix})^2\]
\[cos(2x)+isin(2x)=(cos(x)+isin(x))^2=cos^2(x)-sin^2(x)+2icos(x)sin(x)\]
Take either the real or imaginary part of either side

Answer 11

\[e^{i(a+b)}=e^{ia}e^{ib}\]
\[cos(a+b)+isin(a+b)=(cosa+isina)(cosb+isinb)\]\[=cosacosb-sinasinb+i(sinacosb+cosasinb)\]

Answer 12

Wait, the question is that I want to memorize the double and half angle identities.

Answer 13

My favorite way to recall the Sum and Difference formulas in one beautiful diagram: http://math.stackexchange.com/questions/1292/how-can-i-understand-and-prove-the-sum-and-difference-formulas-in-trigonometry/1342#1342

Answer 14

@nincompoop seconded.

Answer 15

@mathteacher1729 It took me a while to memorize the sum and angle identities, but I have already achieved them. :)

I'm currently stuck on the half and double angle identities.

Answer 16

Half angle formulas are exactly the same thing as double angle identities, just divide all the angles in the equation by 2!

Answer 17

How does memorizing Euler's Formula help?

Answer 18

So you can derive the double angle formula yourself (it really helps for cos(a+b), sin(a-b) etc. also, so it's good practice)

Answer 19

i would never waste the brain cells
google, or learn how to get from one to the other

Answer 20

Yes...\[\rm \sin(a +a) = 2\sin a\cos a\]

Answer 21

but who can remember for example "half angle formula" for tangent, and who cares?

Answer 22

Half-angle formulas are the real trouble.

Answer 23

The half angle for tangent has a really nice visual as well. :)
http://mathandmultimedia.com/2012/05/03/proof-tangent-half-angle-formula/

Answer 24

I wish I could medal you for the links you sent me in the message @nincompoop ;)

Answer 25

You may enjoy the book "Proofs without words" by Roger B Nelsen http://books.google.com/books?id=Kx2cjyzTIYkC&lpg=PP1&pg=PR9#v=onepage&q&f=false Beautiful stuff, good exercises in visual thinking and useful for recalling some identities or getting you a starting point to derive what you need. :)

Answer 26

Books = Money required. :(

Answer 27

lol

Answer 28

Most of the book is available for free on google books.