Identities are cancer

>>8802923
> switch to rational trig
> all identities follow directly from exponential identities

>>8802923
>memorize
you don't have to memorize any of these you idiot
you only have to prove them
all you need is sin^2 + cos^2 = 1 which is the definition of cos

File: image007.jpg (324KB, 1184x906px) Image search: [Google]

324KB, 1184x906px

>>8802947
OP picture isn't related to the point.

This one is though. Memorizing this shit is cancer

>>8802923
>>8802969

You fucking brainlets, you are supposed to be able to conclude those yourself not memorize them.

>>8802923
>memorizing identities
>memorizing anything
fucking brainlets

>>8802923
You are retarded. The only part where you should make an effort in maths is knowing the BASIS. When you know the BASIS almost everything can be derived from that.

To know integrals you should practice differential calculus 1000 times, then you can start doing antiderivatives. There are general methods of antiderivation and you SHOULD know the origin of them. Fortunately the proof of those methods are based on precalculus ways.

Fukcing brainletsdt

>>8803010
Im sorry you like wasting your time anon.

I'll stick to my way of just ignoring questions that involve identities and just solving questions that require actual knowledge of techniques like usub and by-parts and partial fraction.

>>8803023
>wasting time
I literally studied all my yearly math course in 2 months you retard. Also physics and chem is fucking easy now that the math part is trivial.

Do what you want. Brainlets tend to want thiings now "buaah!" lmao

>>8802923
i'd bet money it was an american that made this post

>>8802923
All you need is
[eqn]e^{\mathrm{i}\theta} = \mathrm{cos}(\theta) + \mathrm{i*sin}(\theta)[/eqn]
[eqn]cos(x) = \frac{e^{\mathrm{i}x} + e^{- \mathrm{i}x}}{2}[/eqn]
[eqn]sin(x) = \frac{e^{\mathrm{i}x} - e^{-\mathrm{i}x}}{2\mathrm{i}}[/eqn]

Which are all relatively easy to prove when you know Power series or even Taylor series.

>>8802923
>>8802969
>memorizing
You only need to know one or two identities in order to derive all the others.
If you actually understand what all those trig functions and notation mean, then you can come up with all of these identities without memorizing any of them.

>>8802923
>right click
>image saved
Thanks anon, I can add these to my repertoire

>>8802999
Nice get.
Reasoning is more important than memorization, but a good memory is undoubtedly a huge asset

>>8803372
Okay, then prove this one for me

[eqn] cos \theta = \frac{1}{1+\tan \theta \tan \frac{\theta}{2}} [/eqn]

>>8803442
It's tedious and not really useful, but you get around to that relatively easily.

>>8803477
>being this ignorant about the usefulness of this identity

>>8802923
Literally the best part of calculus, just a blunt memory game on which I can score an A+

>>8802923
you know you can derive all of those extremely easily through complex numbers right?

i mean, if you didn't know that you would be a high schooler. and we know those things don't post on /sci/ :^)

>>8803398
How.

The only ones you need to memorize in my experience are the pythagorean and the sum of angle identities, and you can easily derive the rest from these, and then check out "osborne's rule", which basically means with the above two you can also derive all the hyperbolic ones too.

im gonna derive one for fun without using memory

[eqn]\int \frac{1}{\sqrt{1-x^2}}dx[/eqn]
Let [math]x=\sin t[/math]. Then [math]1-x^2=\cos^2t[/math], and [math]dx=\cos t dt[/math]. But the former also implies that the latter is [math]\frac{1}{\sqrt{1-x^2}}dx=dt[/math]. Hence
[eqn]\int \frac{1}{\sqrt{1-x^2}}dx=\int dt= t =\sin^{-1}x+c[/eqn]

>>8802923
>tfw taking 2 classes right now
>advanced cryptography
>calculus II
>failing one have an A+ in the other

wana guess which is which?

the 500 level crypt class is some of the hardest work I have ever done in my life and I am crushing it
meanwhile taking a fucking freshman catchup course and I can't pass the tests because of shit like this

its a joke

>>8804798
Could that imply that the Cryptography course is low-level?

>>8804769
this, and also learn the trick for inverse functions to use that if, say, [math]\sinh^1(x/a)=y[/math], then [math]\sinh y=x/a[/math], which is easier to differentiate, integrate or whatever

>>8804809
its a graduate level cryptography course so no

the main issue for me is that on the tests I have to remember how to do things that I haven't done in math for almost 15 years now
things like identities and remembering specific rules for integration ect..

these are things that I can look up or have a computer do in 2 seconds but they expect you to memorize how to do them for exams
and then the exams are worth 60% of your grade

which makes no sense