Proving some Random Trigonometric Identities

[xcrgames]

@patrickJMT you improve my math skills and my sarcasm. I thank you.

[KaeruMiyano]

it's so fun when you understand; I wish that the test would be fun too 8/ lol

[AsxZ19]

Wow i was stuck on this question.. and u happened to show the solution to it

(i forgot (a+b)^2 = a^2 + 2ab + b^2 ..... Thankk you soo much!

[hoseinqadam]

wow at 3:01 did he say "So lets see if we CAN'T do another" ?????? : (

I played it more than once and was hearing the same thing.

[grate79]

wow it all seem so simple, but i can literally do hours of problems and never get one righ :'( *notfrustrated at all*..

[MetallicSisters]

thank you very much !

[FrenchMrToast]

why is "the six pack 'shortcut?' " a suggested video

[iStandAsEl]

again and all these problem i be working on the left side but im going to do the same on this side, ... hahah

[SmileForPink]

Math is so tedious. I made a huge mistake by taking easy classes senior year and skipping Calc AB/BC. Now I have to relearn all this stuff because my college requires us to take a placement test and I did horrible the first time! Word to the wise, DO NOT stop at Trig if you have time to take Calc and DO NOT skip math the year before you go to college. Yeah, I graduated with honors, but now I'm screwed and my summer is filled with math which I do not like!! :( Patrick makes it better though!

[NotoriousB3]

fuck you sergia sanchez, mormon fuck

[staples2704]

fucking lefty

[THEBLACKANDGOLD45]

Dude you are a lifesaver you helped me on my final

[omari1555]

i love you

[hsanches1990]

I don't understand why (cos + sin)squared in the denominator becomes 1 + sin 2... shouldn't it become just one instead? cos(squ) + sin(squ)=1 ?

[templar19]

@hsanches1990 (cos + sin)squared = (cos + sin) x (cos + sin), and you have to use FOIL to expand that. Google 'FOIL math' if you don't know what I'm talking about.

[iHsg16]

i got confused after 2:20... thumbs up if you agree

maybe i should study more :/

[weatherallc05]

this is very difficult, but also very enjoyable to me. i know the standard identities, and there are times when they can get you out of jail. many times, even when it doesnt seem that direct a solution

[adreanmarie]

well I wish I can "play" around with these alot, but I think they hate me. :))

[DanaSiew]

amm cud u tell me how to express cos^2x in terms of cos2x please???

[monilove5]

Lord have MERCY!! what can I do to understand this? I like math, but my brain say nooooooooo.

[jejealam]

Marry me!! ;-)

[obliviondick]

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[obliviondick]

iuhiuh

[FuNnYmOjOoO]

can u make a video showing all types of the identities? Thank you =]

[skanecfc]

Good Afternoon

I am really struggling with some trigonometric identities questions, i have been asked to expand, simplify and prove about 10 of these identities and after trying for 2 weeks, watching math tutorials/videos online and asking advice i still don't know how to even start these identities. Please help me, i have put two of my questions below

Cos(2θ) = 2Cos^2θ - 1

Sin(2θ) = 2Tanθ / (1 + Tan^2θ)

Thank You

[whokilledPUNJABB]

@skanecfc  this is the double angle formula like the first thing you're taught

[Jean1juan]

i didn't get the last 1

[5002MasterChief]

Lefty Power!

Thanks Patrick your videos really helped me prepare for my math tests

[MrNikeMike77]

thanks for the help man

[Yingerpoof]

Thank you! I have a test tomorrow but after this I feel a little better, woo hoo!

I hate mathhhh

[Tungchu92]

Is there any identities for Cos(Beta)-1?

i keep running into this one and my dam professor refuses to help by giving us the "you should have known this" card.

please somebody help like RIGHT NOW

[kenisvery]

Can anyone help me to prove this equation. Thank you!

Prove the following identity

(a) SinA/(1 + CosA) = Tan (1/2)A

[djwestbrook36]

ughhh

[patrickJMT]

@djwestbrook36 ughhh back

[djwestbrook36]

@patrickJMT my bad i was just so annoyed that i had to learn this stuff. lol

[patrickJMT]

@djwestbrook36 sorry that you feel annoyed at having to learn!

[djwestbrook36]

@patrickJMT the problem isnt learning. its learning 12 hours worth of material a day while trying to handle a social life

[patrickJMT]

@djwestbrook36 lol, you truly have the most difficult life in the world

[djwestbrook36]

@patrickJMT ok u owned me with the comment, now ill just look away and move on.

:/

[cuppajoesugar]

@patrickJMT lol pwnt

[steelekilla101]

Guess who has a test tomorrow????!!

[LAnonHubbard]

I'm learning calculus and coming to realise how important trig identities are so trying to learn them and how to maniuplate them. There were some I didn't understand in this video, so a lot of learning/practising required. Thanks for showing the process. It's nice to hear you talk through the proofs.

[kookiesncreamx]

can you wear a wig and take my test for me. no one will ever know!

[patrickJMT]

@kookiesncreamx i would draw pictures instead of answering anything

[lalosand4487]

"Go sine Cosines"

[tailzz14]

thank you soooooooo much :) without you i wouldnt be going to college

[patrickJMT]

@tailzz14 hahaha i think u would be doing ok : )

[SatanicEvilDemonKid]

Thank you so much!

With your math videos i was able to complete my entire exam review without my textbook or notes!!

You are so great at explaining concepts.

[monahlhyzza]

amazing!

[sweetkisses1818]

I fkn love you

like honestly you are the best math teacher EVARRRRRRRR

[harpinduh]

i love identies :D !!

[patrickJMT]

@harpinduh haha

[BatistaR0X]

a lot of my friend whos left-handed are fking smart.

[OhEmGeeitszHend]

can u put up harder examples plzzz? this is way more helpful than my teacher

[Di3inH3ll]

THANKS A BUNCH you are more helpful than my $35/hr tutor =p

[patrickJMT]

@Di3inH3ll that's why i charge $80/hour

[BatistaR0X]

@patrickJMT LOL.. hahaha

[mustafamufasa]

on the first example why did you multiply to terms on the left. how does that make the right side equal. shouldn't you multiply the dominator on the right side of the equation.

[djdesignerlab]

these are too easy. Show some hard sums.

[genciT5]

Hello Mr. Patrick.Can you tell me: what is : sinX cosX = ?

Thank you

[RobSchneeberger]

i like how all the examples i do in class at MSU are just the hardest shit, they don't ever give you a simple identity, it is something obscure that involves numerous steps of algebra within one identity, so frustrating, it is to the point that it ruins the purpose of the assignment, like busy work, god i wish i had someone explain these to me that isn't a college professor that couldn't care less whether the class (or me) understands the material

[boxoflols]

Ok dude. I only know the main ones. like tan theta , and the pythagorean one... I never seen the "little trick" identities. Could you pleas show all the little ones in another video?? I waste alot of time doing this crap :( I wanna finish faster. Thanks

[snigloid]

Ok on the 2nd problem how do you know that 2sin0cos0 is sin(20) because i'm comletely lost on how you got that plz let me know how thanks.

[AutopsyReport22]

Why didn't you do any half angle identities which are harder?

[objective33]

your examples are too easy though, not practical for tests or assignments, thus rendering the lecture useless.

[patrickJMT]

@objective33 so do not watch. pretty simple, eh? go troll some other videos.

[Sarothesnauz]

@objective33 not cool man, he's trying to do a service here.

Not a lot of people go out of the way to do this kind of stuff.

[harajuku0618]

>.< Math.

[ronnilljane]

i like it ... do you had a copy when you do this ?

hahaha ..

[y318]

Could you please prove (1-cosT)/(1+cosT)=cotT*cscT ?

I think it is impossible. I got that one in a final exam and I got it wrong. Nobody can do it.

[Cammie010]

@y318 Hi. I can prove it for you. :)

For the equation on the left, multiply the numerator and denominator by the conjugate. (1+costT or 1-costT). You should get (1-cosT)^2/(sinT)^2. Use the pythagorean identity for cosT (u should get a root). For the equation on the right, just use the reciprocal identities.

The right equation and the left equation equal the same thing, therefore they are equal.

I hope this helps. thanks :)

[oldtajikboy1989]

my question is when you simply factor the negative one . then why don't you change the minus sign to positive inside the bracket

[linkinlogstm]

lol

the left side is slightly more complicated and... whats wrong with left handed math mathematicians huh?

[Astatine0936]

i do believe unique is a compliment

[PlasticCoffee]

Left-Handed Mathematician

...unique

[squirldude]

@PlasticCoffee

or maybe he's writing everything mirrored with his right hand and flipping the image. That would be more unique, eh? :D

[PlasticCoffee]

Haha

Interesting thought

[JesusChick316]

it's comforting to know that 16,500 don't understand this either...lol

[JLMannequinFrightful]

I am so much less confused! Thank you, thank you! Exam this Friday! FML

[nickol0l23]

ty so much =P

[dailybrother]

does it matter as to which side you start from? i would like to see an example involving tangent, cotangent, cosecant, or secant if you got the time, could you do an example on that please? thanks. these examples clarified the basics for me really well.

[helenJuice]

you have been truly helpfully to a lot of us out here, keep it up.

and thank you so much for doing what you love most.

[azerbaijan93]

thanks alot! :)

[identity21121]

will you prove that 2sin()cos()= sin(2theta)

[xHiE48]

Why 2sin()cos() = sin2() ----> ???

it's like this..

From the sum and difference of angles, we know that sin(A+B) = sinAcosB + cosAsinB...Now, sin2() is what we are looking for. To prove it, let sin2() = sin (A+A) then substitute values. We now get sin()cos() + cos()sin()

We now have 2sin()cos() because 2sin()cos() = sin()cos() + cos()sin()

I hope I made myself clear. :D

[Zackarius14]

lol sin2() equals 2sin()cos() that's one of the basica rules

[saemusic22]

i think my grade in math went up a letter grade because of you. THANK YOU

[wlryn6]

thanks dude wen my teacher went over this with one of his lectures i really did not understand it thanks agian

[kebabsallad]

Is it possible to prove these identities by the unit circle ? Or are they to complicated for anyone to define there ? Would be cool if it worked, especially for me who suck @ AlgeBRA :S

[prodigyshikamaru]

this is so awesome!!!!!!!!!!!!!!!!!!!!!!!­!!!!

[patrickJMT]

*hugs* Michaela (- in a non creepy way.)

i agree, most people do suck.

but when you run across you the cool people, be it all so rarely, it makes everything worthwhile.

[BerPC96]

bravo bravo thanks again man for you help

[combool]

nice i understand i will tell my class made about this.thanx

[damasta00138]

For the first problem, it is easier to cross-multiply :D. You get: tsect-1=tsect-tsectcost

(sect*cost=1 therefore)

tsect-1=tsect-1

[patrickJMT]

ok!

[patrickJMT]

sin(x+x) = sinxcosx + cosxsinx = 2sinxcosx...

so now ask:

why does:

sin(x+x) = sinxcosx + cosxsinx?

[KoyoteHokage]

and btw how does it change from 2sinxcosx to sin2x... sorry my math isnt that good :(

[KoyoteHokage]

isnt sinx-cosx X sinx+cosx=(sinx-cosx)^2???

[qaddodi]

nooo

cuz sinx-cosx* sinx+cosx = (sinx)^2-(cosx)^2

while (sinx-cosx)^2= (sinx)^2-2sinxcosx+(cosx)^2

[Birdboy07]

Thank you so much, we needed to make a video project for school solving some trig examples. Hope you dont mind if we used some of these in our project :)

[patrickJMT]

nope i dont mind! you could also tell your classmates about the wonderful resource that you found though : )

[martialrockarts2]

wow this helped clear up some questions that have really confused me tyvm i think i might just get it now

[ascendedsayian101]

Man let me start of by saying math sucks, lol jk, welll..nott really, this helped so much though thankssss

[arven34]

hey can you give me equivalent of Proving Random Trigonometric Identities plss i want to know a lot of trigonometry for me its soo challenging

[Formesse]

I love these videos, saved my life cause it makes sence (my math teacher I think doesnt understand that there are a gajilion learning styles = )) ps thx a million

[XxdementedDOLLXx]

It looks so easy when you do it!

...I think what my problem is that I need to know what my properties are.

Great vid though! It helped a lot.

[sakuranbo888]

oh thanks... my maths teacher is so crappy

[patrickJMT]

sorry to hear that the teacher sucks! just come home, and get a little 'patrickjmt fix' and you will be ok!

[ionglacier]

sum1 plz do the question below, its worth alot of marks n i couldnt figure it out

[ionglacier]

hey dude can u plz solve a trig for me i couldnt solve it no matter how i tried n i no for sure that LS=RS

tan(3A) = (cos(2A)-cos(4A))/(sin(4A)-sin­(2A))

[kst223]

god i love youtube, thanks so much for the help :)

[patrickJMT]

yes, now you have an excuse to waste so much time on here!! : )

[ajithla]

you are doing a very nice job

it really helped me alot

[JMislove07]

wow, you helped me soo much.

i swear i could sit on here all day and watch your examples instead of writing the hour and a half long note my advanced functions teacher shows me each day and learn way more from you.

thanks : ]

[Conceptzx2]

thanks, hate proving identities it's always hard to know where to start.