Trigonometry identity review/fun | Trig identities and examples | Trigonometry | Khan Academy

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Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!

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[Galdring]

I mean... The math is pretty straight forward, but how on earth do quickly gain an overview of this? That Khan can effortlessly derive all these formulas, keeping track of which have already been derived, and how he can use them to find new ones, is amazing to me!

[AK-uocm]

This was absolutely exceptional. I love that feeling when your teachers tell you to memorise a formula without really telling you why, and then after you find out the proof you have the "ohhhh" moment.

[mindsprings]

If this video didn't exist, I may have committed seppuku trying to learn this shit

[misscocotl]

amazing! all looks so easy and nice! But by the time O try to put into my homework is just awful.I think I will cry.

[keanuoliva]

Thank you for showing me how all the identities connect together. This was extremely helpful. 

[khanacademy]

@jus400track I try though, but, yes, it is getting difficult now

[TheDkmariolink]

This shit is so hard... This alone will probably make me fail my math test >.>

[ryanhillard]

This is such an easy way to memorize and more importantly understand these identities. This video was recommended by my physics professor to help review trig identities and I can already tell this will make a big difference. Thank you Khan!

[suddencuriosity]

Wow I never saw it that way! It's amazing to see all of these formulas have connections to see that somehow these aren't just random and that there's a whole rabbit hole to discover them all. Great video.

[jumpmanyang]

WOW, your voice in is the Khan PHYSICS videos too!!!
Is he a genius professor or sth?

[collcool]

@dragonpaint37
The brackets are being raised only to the power of one. Anything raised to the one power is itself.
(1 - sin^2 a) - sin^2 a
1 - sin^2 a - sin^2 a
1 - 2sin^2 a

[JustAG]

LOL I almost thought the video ended at 6:55!!

[Phil]

@dragonpaint37 because it's a minus sign that follows the bracket, not a multiplication sign... therefore you do not distribute...

[PurpleBandit]

@collcool0 actually anything raised to the power of zero is one. Anything raised to the power of 1 is itself. However, in this case, 1-sin^2 a is 1 because it is a trig identity.

[theopenacademy]

Thank you so much sal and all those who work effortlessly to make these vids happen!! Love you all. Its a sad time in education when educators like my teachers cant satisfy my questions on where these came from, but on the other hand there are educators such as yourselves that actually care about spreading understanding instead of just making little robots that can spit out some answers.

[TubbsCustard]

I love the timbre of your voice, sire

[falpalemily]

It's too bad that Khan can't do a video on how to write papers. I'm struggling with mine...

[mathfacts]

Double angle identity
Tan(2@)=2tan(@)/1-tan^2@
Can we verify it at @=45degree?

[JSnyder]

@JSnyder49428

3) You aren't from MI are you? 3 of the 5 professors I have right now are hunters. BUT, don't you think there are a plethora of other factors influential on whether or not people hunt? Take location for example, how many universities are near hunting grounds? I could go on and on about reasons like this...

4) How do you determine "intelligent people"? by the awards they've received? the subjects they teach? How successful they are? And I ran out of room again

[idster]

@JSnyder49428 yes, i meant two*. intelligence & empathy toward animals are correlated. i'm not saying hunters tend to be stupid. they're independent, perhaps contrarian, people. they may be smarter than the average. but very smart people tend not to be hunters. what percentage of college professors or macarthur grant winners do you think are hunters? a far less percentage than the general public, and not just cause they're too busy.