Trigonometry to Memorize, and Trigonometry to Derive

Ackbeet

MHF Hall of Honor
Jun 2010
6,318
2,433
CT, USA
I have attached a pdf document containing the vast majority of trigonometry I have needed to know on a working basis. The first page consists of trigonometry I think everyone should have memorized. I have never needed to have anything more than the first sheet memorized for any application. The second page is a non-exhaustive sheet of most of the trigonometric identities that I have found useful, and a few more besides.

It is my opinion that a student who memorizes the first sheet, and can derive anything on the second sheet, has a fairly good grasp of trigonometry.

I hope this proves useful.

View attachment Trig Sheets.pdf
 
Jul 2011
1,254
389
Belgium
I think it's very good document :).
(Do you have more documents for other subjects maybe?)
 

Ackbeet

MHF Hall of Honor
Jun 2010
6,318
2,433
CT, USA
I think it's very good document :).
(Do you have more documents for other subjects maybe?)
Thank you very much.

I don't really have any others like this one. The reason is the only courses I have taught were Calculus, and this was intended as a review sheet for incoming freshman who were taking my class. I do have problem-solving stickies in the Other Topics and Advanced Applied Math forums. That's about it. Chris L T521 has a very good DE's tutorial, and there's already a LaTeX tutorial and a Calculus tutorial. There's even something in the pre-algebra and algebra forum as well as the linear and abstract algebra forum. So that's most of the forums that I pay the most attention to that even admit of such a document.
 
Apr 2012
19
0
United States
I had an identities quiz, and I used your sheet to help with memorizing the formulas. Thanks a ton! Any pointers on memorizing the unit circle :9
 
Jun 2012
7
0
Goonellabah, NSW, Australia
I find this enormously useful (and encouraging! as I can see how far I've come in a relatively short period of time; and salutary! as I can see how far I have to go before my exam on 17th July)
thanks Ackbeet: thoughtful and very useful!

Godfree
 
Jun 2012
616
115
AZ
I had an identities quiz, and I used your sheet to help with memorizing the formulas. Thanks a ton! Any pointers on memorizing the unit circle :9
You should be able to "visualize" the unit circle, and know which angles correspond to \(\displaystyle \frac{\pi}{4}\) or \(\displaystyle \frac{\pi}{3}\). Also, by definition, the sine and cosine are the y- and x-coordinates of the point on the circle. No memorization needed...
 
Aug 2012
23
0
Nepal
This really helps! Thank you for sharing your knowledge here. Is it free to ask you anything here that involves mathematics?
 
Apr 2012
6
0
In your dreams
This really helps! Thank you for sharing your knowledge here. Is it free to ask you anything here that involves mathematics?
Yeah its absolutely free,though you can donate them some money if you think so but its not necessary.
But yeah you cannot use it as a homework completion site ;)
 
Jun 2013
43
0
Ireland
Thanks for this helpful document. Much appreciated.
 
Dec 2013
2,002
757
Colombia
I would add to the second page $$\cos{(A-B)} + \cos{(A+B)} = 2\cos A \cos B \\
\cos{(A-B)} - \cos{(A+B)} = 2\sin A \sin B \\
\sin{(A-B)} + \sin{(A+B)} = 2\sin A \cos B $$
 
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