Verifying trigonometric identities, hard with multiple steps

[@brianmclogan]

Don't always pick what you think is the most complicated side - kzbin.info/www/bejne/e2aycp-Op9eqg80

[@chumdog6060]

Ok but wouldn't it just be easier to jump infront of a train

[@brianmclogan]

I do not think so

[@blockobutter]

Yea, I think it would. Plus, unlike these proofs, it would have an actual effect on your life.

[@Coughingcatbleh]

You are my hero lol

[@fankpop3892]

Chum Dog Block o Butter I wish both of you go to jail for this! I bet you don't even know to become successful in life like this smart gentleman (KZbinr) is

[@katiestone4239]

Jail? Isn't that a bit too far?

[@slyliezeroseven3696]

I'm genuinely convinced whoever came up with this was high off of several different shrooms dipped in wax

[@Cruzaman4040]

They did it on purpose to confuse people with fake math

[@djboo7779]

It's funny bc whenever a teacher teaches this in class, or does a problem on the board, everyone is silent. Like we're all just watching like wtf how

[@Cruzaman4040]

Fr it’s just magic. Doesn’t make any sense

[@PhobiazBro]

Just accepted that I’m taking an L on this unit ... oh well

[@isaacjones6601]

High school musical “ we’re all in this together”

[@PhobiazBro]

Finished with an 83... anything’s possible 😔

[@thinhphan3816]

im barely scratching a D in math

[@spartandeceit9146]

yup did trig about 3 years ago. took that L so hard.

[@SUB0SUN]

Well now it’s online😄

[@rav.n.9104]

All of this is literally "wait you can do that?!"

[@jimmyjohns850]

Exactly how im feeling bro

[@memeherepancakes5203]

4:54 Thank god someone spotted that otherwise I would have to restart my memory again for math.

[@edo74859]

lmfaofoa ik i had to come down to the comments because I didn't notice he messed up

[@sophiaarias9341]

i was stressed out for like 10 mins trying to find how he simplified cos^2x to csc^2x 💀

[@SweetStickmann]

THANK YOU, I was looking up how he did this.

[@error_606.]

frr 6 years later but we all felt that stress

[@rubycastillo1898]

I felt so stupid because me and my friend were literally confused and then everyone else was like, "OHHHHHHH OKAYYYY." I'm here with my friend and we are literally struggling. Not gonna lie i cried inside my head

[@erikp9014]

It’s amazing how when I watch your tutorials, I have a slight clue of what you’re doing. I just need to keep watching multiple times to understand. When my professor teaches me, I feel completely lost throughout the whole lecture and always tell myself: “How did he do that”, “I’m going to fail this class so hard 😭”. All he does is solve the problem in his head but doesn’t explain shit. Like, is this really college and how all professors teach or did I just get unlucky?

[@riyabawa5382]

#MathHelpers#MathHelpers

[@FuzzyMonkey95]

Hey! I know you commented this quite a while ago, but not all college professors are bad. Some are a better fit for you than others, and that is ok! Someone else in your class may really jive with the teaching style while you don't. I hope since this comment you have had better luck!

[@stonercat1232]

I hope this isn’t all professors

[@FuzzyMonkey95]

@@stonercat1232 I can assure you that it isn't! My calculus professor this semester explains all problems very clearly and very well and is constantly asking if we have any questions. We even have one class a week dedicated just to asking questions from the homework or otherwise.

[@michaeltnk1135]

Because you can’t rewind what your professor says

[@TeaWithExtraLemon]

Because of Corona I'm having to learn this without a teacher... RIP my A in math.

[@lily-ne3lb]

same lmao

[@ryanmcnally5853]

still quite relevant

[@dillonhaynes6427]

i feel ya

[@neonlights3814]

Who told you that you will get A with a teacher , hahaha we barley passed its quiz with a teacher

[@renk9290]

Same😭

[@King-gv4lg]

This is the one of the most bullsht thing that one is gonna encounter studying cal, and im under engineering

[@masaohonda6145]

Who else is gonna fail their final tomorrow!🙋‍♀️

[@ramihadey7142]

How'd yours go? I'm taking my precalc final tomorrow 😟

[@trollscream8607]

123 321 how’s yours

[@ramihadey7142]

@@trollscream8607 oh I got like a C but it's fine

[@chesterthepro28]

Im gonna fail math exam in few days only cuz of this STUPID TRIG UNIT!

[@DemonMage]

2 weeks from failing. Woot.

[@mov1ehunter]

Worst part 0:04 to 6:53

[@brianmclogan]

haha noted

[@Arycke]

He's trying man. And giving some knowledge so that's a good thing. Didnt think it was that bad.

[@HeyKevinYT]

Arycke By “worst part,” I think he meant the most difficult part, which is the entire video. He’s not saying the lecture is bad

[@Arycke]

@@HeyKevinYT twas implied in my comment. He got told his whole video was shit and I said he was trying. Yeah I know.

[@tmwbatman1160]

Arycke it was that bad.

[@saintsour124]

I don't know if you learned this but my teacher gave a cool way to memorize the Pythagorean identities there is only one thing to memorize which is sin^2x + cos^2x = 1 and from this, you can get the others, btw(you need to memorize the reciprocal identities and tangent identities which is easy) the first thing is that you need to do is put sin^2x as a denominator for each identity: sin^2x + cos^2x = 1 sin^2x sin^2x sin^2x using the reciprocal identity to solve this sin^2x over sin^2x would simply equal 1 then cos^2x over sin^2x would equal cot^2x finally, 1 over sin^2x would equal csc^2x and then you put it all together 1 + cot^2x = csc^2x WOW, THAT LOOKS FAMILIAR you then do the same but replace the denominator with cos^2x if you do the same process and use the reciprocal identities at the end it would look like tan^2x + 1 = sec^2x the math is down here | | V sin^2x + cos^2x = 1 cos^2x cos^2x cos^2x sin^2x over cos^2x would equal tan^2x cos^2x over cos^2x would equal 1 1 over cos^2x would equal sec^2x now when you put it together it equals tan^2x + 1 = sec^2x hope this helped :)

[@vincelorenzang664]

Mind blowing bro nice one

[@rodrirodriguez7298]

I paused the video and got stuck on the problem for like 15 minutes trying to figure out the csc lol. Then I heard he said cos plus sin and I was like o he just wrote it wrong. Then that girl caught his attention on it, thanks lol

[@brianmclogan]

sorry about that, it happens from time to time

[@PolarApocgaming]

Same

[@razortongue5813]

lmaoo, same here. Plus my native language is not english so i was like "omg what did just happen here i miss something????" lol

[@adityaalok7113]

this is just clickbait brother see the thumbnail,I am sure thumbnail is edited 😂😂

[@Gerud0]

Not gonna lie you've definitely helped me this semester. You're like a tutor I can rewind without feeling like an idiot lol thank you

[@PrinceTae]

Welp... I’m here for a good time not a long time

[@WTHnada]

i dont even know what i just watched. Still confused. didn't fix anything, really. :( i have a test next thursday :/

[@MIZZIJR]

I feel like we have the same class.

[@Ang-cu5es]

Hey, tomorrow is my finals and I just wanna thank you for your helpful vids. It got me through the entire semester, always there whenever I needed extra help, and very thorough. Thanks, Mr. Mclogan!

[@brianmclogan]

you are very welcome!

[@Haza-rp1cb]

howd you do lol

[@yourtypicalfan5283]

@@Haza-rp1cb I ended up getting a D on my finals 😂 but 4 years later and I finally graduated college lol

[@Haza-rp1cb]

@@yourtypicalfan5283 lmaooo congrats my guy 🔥

[@yourtypicalfan5283]

@@Haza-rp1cb lol thanks 🙏

[@Skylar854]

Thank you so much for posting! Your the only math teacher I actually understand

[@D-PRYDE]

*Quick Question:* How do you get *csc^2 theta* from *cos^2 theta?* 🤔 3:54 *Update:* Thank you for fixing it to *cos^2 theta* ✅️ 4:54

[@Peanutz4life]

That cos change tho CSC messed me up. Thank god someone in ur class pointed it out.

[@jasonlassiter9229]

To me, proofs are the hardest and most tedious part of Trigonometry. Good luck to anyone taking any exams this week?

[@riyabawa5382]

#MathHelpers#MathHelpers

[@nicholasdomol574]

All of your videos are extremely helpful. I’ve never felt more comfortable with math than I do now. Thank you sir. I am truly grateful.

[@brianmclogan]

you are very welcome! happy to be able to help you out!

[@paigesmith9800]

thank you so much for posting these videos! i spent an hour and a half watching pre calc and trig videos the night before my final and you're the only math teacher i understood completely

[@brianmclogan]

+Paige Smith happy to hear my videos helped you out, how did you feel you did?

[@paigesmith9800]

my teacher said i didn't fail, so i'm stoked! i'm pretty sure i got a C+ 😁

[@rajveerbhardwaj8470]

Here to study for my Pre-Calculus test tomorrow thank you !

[@harshalijagtap9838]

im dying right now! I have A level in Jan and this trigonometry is making me cry now ! this thing is hard man.

[@brianmclogan]

it is keep practicing, I remember learning this stuff and it took me many examples to get it right, check the playlist link at the end of the video for many more examples or search #Analytrig

[@harshalijagtap9838]

ill try. thank you

[@manchita88]

Just try to learn the identities and have a little malice and it will turn out to be really easy!! I wish you goodluck!

[@dilshanweerasinghe5916]

3:54 CSC is actually supposed to be cos

[@brianmclogan]

thank you!

[@vondrez]

@@brianmclogan no u!

[@thesunfirecape]

Lol

[@claytonborges6534]

Posted in 2013 helping me in 2019

[@satrickptar6265]

To make it easier, we can use conjugation at the very beginning. We can multiply (1+sinθ)/(1+sinθ) to lhs so we can get a 1-sin^2θ as the denominator and we can now use Pythagorean identity to make it cos^2θ. We now have [cosθcotθ(1+sinθ)]/cos^2θ then we can simply make it [cotθ(1+sinθ]/cosθ. Our next step is to distribute cotθ so we will have (cotθ+cotθsinθ)/cosθ. We can now make cotθ into cosθ/sinθ by using the reciprocal identity of tanθ. After using the reciprocal identity, we can now factor cosθ to make it [cosθ(1/sinθ+1)]/cosθ. We will ended up with 1/sinθ+1-1 (I just recently put -1in the equation because you'll only need it when you're gonna cancel out 1). We can now turn 1/sinθ into cscθ by using the reciprocal identity of sinθ and there we have it!. cscθ=cscθ , ' , LHS=RHS ; identity

[@asgardian12]

Excellent explanation, thank you! A minor tecniqual comment is for the last step. Personally, I find it easier to think this way: a/b = a * 1/b, so your (1-sin(x))/sin(x) / (1-sin(x)) is simply (1-sin(x))/sin(x) * 1/(1-sin(x)) = 1/sin(x) -- no need to think of it as multiplying by 1/(1-sin(x)) / 1/(1-sin(x))

[@brianmclogan]

thank you and appreciate your point and feedback

[@elliew.738]

Thank you so much for posting this video! I found tons of KZbin videos about trig identities, but this was the first one to acknowledge how to actually solve them.

[@Kapss23]

I gotta quiz next period I’m gonna cheat wish me well 😂

[@riyabawa5382]

#MathHelpers#MathHelpers

[@gurleenkaur3223]

thank you so much!! I have been watching you since pre-cal and ever since, you have been a great guide and solver to my math stuggles. I appreciate the work you put into this!

[@brianmclogan]

You are so welcome!

[@MrHighFRUCTOSE]

You made this so much more confusing than it needed to be by saying things incorrectly

[@brianmclogan]

what did I say incorrectly?

[@fabriziootey8684]

everything up until the 2 min mark

[@fankpop3892]

Fabrizio Otey Is your name "MrHighFRUCTOSE"? He wasn't asking you in case you haven't notice...

[@djboo7779]

Fan KPop if you were to apply your own logic...then fabrizio otey wasn't asking for your reply.

[@fanimeproductionst.v.3735]

@@djboo7779 OOOH SHIT

[@solitudeinarctic787]

U r a life saver but this is not ur best video.

[@Rebeljah]

This actually helps a lot, I need to focus more on trying to combine fractions before contuning. Things start to stack up then

[@riyabawa5382]

#MathHelpers#MathHelpers

[@kobynmalone2134]

Bro I spent ten minutes trying to figure out how you pulled a csc out in that. Obviously I couldn't so I just kept watching to figure out that I was on the right track anyway. Thanks for the help tho, I know I'm on the right track for my exam friday.

[@brianmclogan]

Timestamp?

[@kobynmalone2134]

@@brianmclogan 3:45

[@lucapointcom]

I see a lot of complaining about how you did it, but it's a different approach and shed light on many methods I have never even considered (mainly multiplying by the reciprocal). Really helpful :)

[@brianmclogan]

thank you! yes sometimes one method is faster than an another or easier to work with or understand.

[@irasemoomoo135]

You’re helping me learn precalculus in a whole new decade

[@gregorysmith9441]

he is the greatest teacher i never had

[@Anon-eg5iq]

hey! i know it’s been 8 years, but i think i found a quicker way. so for the first term, multiply both the numerator and denominator with (1+sin(x)) aka the conjugate, and convert cot(x) = cos(x)/sin(x). we now get (1+sin(x))(cos^2(x))/sin(x)(1-sin^2(x)). we can convert cos^2(x) = 1 - sin^2(x) due to the identity, so (1+sin(x))(1-sin^2(x)/sin(x)(1-sin^2(x)). after eliminating 1-sin^2(x), we get (1+sin(x))/sin(x). now we can just regularly subtract that with 1. 1+sin(x)/sin(x) - 1 = (1+sin(x)-sin(x))/sin(x) = 1/sin(x) = csc(x). i really love that when proving trig identities, we can have multiple ways of approaching it!

[@penguin4life212]

this is so complicated, but your videos were very helpful!

[@brianmclogan]

happy to help!

[@manishathakur20]

No, videos were complicated 😵😵😵🥴

[@ChristAliveForevermore]

I love when something others call hard become easy with practice. Gives you the illusion of being smart 🤓

[@AldousSeriousPunch]

My method is a little bit different, I multiply with the conjugate both denominator and numerator by 1+sinø so the denominator become 1²-sin²ø = cos²ø and then simpify to get 1/sinø + 1 - 1 = 1/sinø = cosecø

[@Anon-eg5iq]

lol i thought of that too

[@farahmelissabharambeyguibo2982]

What i am doing is writing a sheet with all the possible ways to solve identities such as multipling everything by the denominator of the numerator like he did with sin/sin. I also wrote down multypling top and bottom by the reciprocal of the denominator. Theres also another one where u multiply by the conjugate of the denominator.

[@riyabawa5382]

#MathHelpers#MathHelpers#MathHelpers#MathHelpers

[@amango7551]

0:35 Thanos theta

[@alexd.8554]

Thanks so much! My teacher introduced this fun yet confusing unit on last Friday and he’s planning on making us take the test on it this Friday, so we only had five days in class to learn what the heck is going on. This helped me get the easier stuff on the WS done 😭👌🏽✨🥺

[@chocolatee31]

Good evening sir, may I know at 4:31 how did the denominator became 1-sin(x)? Thank you!

[@EP-wg1pp]

Hi Brian! I'm on to Precalc. Glad to see your venture is going great.

[@julianathornton9226]

Thanks you for the help Brian!

[@bigstuff52]

I learned a ton going through these Identities with you..Thank you sir....Your students have a good teacher..

[@brianmclogan]

appreciate it and happy to be able to help you out John!

[@kobinayler8105]

Can I just ask why at 3:35 does the first cos become cos squared and not cos squared sine over sine?

[@jillianhutchinson4475]

This is so helpful, thank you so much!

[@iZAPMath]

Awesome explanation, Brian! I love your videos! Keep up the good job!

[@riyabawa5382]

#MathHelpers#MathHelpers

[@genesisgallego7029]

Man i feel so confident with these trig unit due to videos like these! Thanks a lot Mr.Brian!

[@brianmclogan]

you are very welcome!

[@No-cg9kj]

3:45 "What's this supposed to all equal again?" When even the professor realizes the problem is a complicated mess of bullshit haha.

[@brianmclogan]

🤣🤣💪

[@jeieee2134]

If I were his student, I would probably clap after being taught that step-by-step (and be in awe too)

[@riyabawa5382]

#MathHelpers#MathHelpers

[@wave5155]

Thanks Brian!

[@shaneisland]

My actual award-winning teacher: You guys gotta work harder and study for the test Also my teacher: Fails entire class and blames us.

[@rickdoesmath3945]

Why blame the teacher if yall failed?

[@Calyrekt]

@@rickdoesmath3945 an entire class failed? what are the odds everyone is just too inept to grasp the concept versus their prof. is inept at teaching it.

[@DavidSolanke]

you're appreciated we love you man thanks for all the time and effort have a blessed day!

[@riyabawa5382]

#MathHelpers#MathHelpers

[@lilianachavana253]

I’m so glad that girl pointed out that he wrote csc in error, I paused the video for like 15 min until I chunked it up as a loss to my understanding.

[@suhaildurrani6181]

thank you so much, I was having trouble with this exact type of question. I think I'll do a better job on my trig test tomorrow.😆

[@bro_vega_1412]

(I don’t want to type θ) Since cot=cos/sin and cos^2/(1-sin)=1+sin,we can get (1+sin)/sin - 1=1/sin=csc.QED

[@samina-minaeheh2541]

I wish this guy is my math teacher

[@pravini]

I just realized that this was 9 years ago. Which means these kids are in their late 20s

[@shrichandchimnani3658]

Guys just practice is all you need,once you get the grasp well onto the concept everything will turn to be easy I'll tell you guys these 4 steps 1.use trigonometric identities wherever you can use them 2.convert into sin and cos 3.take common if possible 4. If nothing works then rationalize

[@diothepoet7311]

You got bunch of difficult kids buddy🤣💓 this is helpful thank you so much

[@riyabawa5382]

#MathHelpers#MathHelpers

[@OMaMaRMY]

Great video as always!

[@s.chauhan6423]

thank you so much this helped alottt

[@grishmashrestha7722]

Can we just change the equation to the simplest form by exchanging it with the trigonometric equivalents and just like canceled the common ones from the numerator and denominator? Like this: cosxcotx/1-sinx-1=cscx cosxcotx/-cos(Since sinx+cosx=1,sinx-1=-cosx) cotx-1(Since negative and positive cosines are canceled) therefore :cscx(Since cotx-1=cscx)

[@hielokasama5574]

Thanks man your nephew sent me here!! :)

[@benedicturban3220]

on the 4th step, why when you multiply cos(theta) by sin(theta)/sin(theta) do you get cos^2(theta)

[@matymbye8989]

I think that you made it much harder then it actually all I did was I changed the denominator to cosine (sine and cosine Pythagorean rule ) then I cancelled out the cosine of the numerator and the denominator , that left me simple with cotangent minus 1 which is equally to cosecant (because of the cotangent and cosine Pythagorean rule )

[@liliacfury]

he has a very different and more confusing way of solving for these then me. Right of the bat I would of multiplied the numerator and denominator of the fraction by the denominators conjugate.

[@brianmclogan]

that's great!

[@isaacjones6601]

How did u got cos squared over sin when the common denominator was sin?

[@DietEwok]

The original term was cosx•cotx; since we are multiplying we don’t need to find common denominators and if simplified its cosx/1 • cosx/ sinx ; multiply tops and bottoms gives you cos^2x/sin

[@shaunsnow2032]

@ around 4:36 mark you have 1-sin theta over sin of theta in the numerator. Then you have 1-sin theta in the denominator. I don't see where that 1-sin theta in the denominator comes from??

[@naokistv]

There’s honestly so much going on and I have a quiz tomorrow. I can’t understand with so many things going on. Is there a possible way to condense it to the very basics?

[@brianmclogan]

yes this is an advanced equation, start simple and work your way up search #AnalyticTrig and you will see all my playlists from easy to advanced

[@jbiliHacker]

very good teacher!

[@blakedunaway5513]

please try using different colors to color code the original/actual problem and the math. Maybe use black for the problem and blue for the additional math.

[@brianmclogan]

appreciate the feedback

[@VesDegree]

I have a question. At 1:30, what happened to the csc theta? You brought down everything else but the csc theta was completely left behind.

[@brianmclogan]

I could had continued writing it, to save time and writing I just wrote the equal signs and prove the left side is equal to the right which is unchanged.

[@marz8386]

This is the sort of math where you have to rely on pattern recognition and it only gets easier with practice.

[@maalikserebryakov]

wrong i have created a perfect method for proving any true trig identity

[@helenavolynets8961]

i came here to get help for my hw and now im just cryin b4 i gotta go to school

[@xiaotu134]

Currently at a 95 and this is my last unit. GG time to tank a shot

[@Ivan_savior]

At 4:30, where did you get the 1 in 1-sin for the denominator?

[@brianmclogan]

Not sure in my phone will have to check in that when I return

[@Luke-kq8gh]

I know I'm 2 years late, but if you look higher up, the 1-sin was in the denominator of the whole thing, he brought it over but did not keep rewriting it for the steps in between.

[@OMaMaRMY]

lmaoooooooooooooooo

[@John-lf3xf]

It's pretty easy thanks

[@arktic_s]

Thank you, God bless you

[@sanwu3412]

Where did the 1-sin theta on the denominator go in step 2 and 3?

[@NaturesZombie]

How do sine and cosine cancel each other out?

[@justachildofGod]

Thank you so much.

[@loisadurlg5789]

I got it, thank you sir brian

[@BigTeddy899]

I’m in algebra 2/ precalculus currently, we’re going to do this soon.... rip

[@thistiem5745]

if you are multiplying 1-sinA to numerator and denominator then denominator will undergo the identity of [1-sinA]2 whole square

[@brianmclogan]

What point in the video are you referring to?

[@thistiem5745]

oh sorry !! u took 1-sin theta in denominator i just thought u multiplied both numerator and denominator with 1-sin theta

[@thistiem5745]

it can be done more easily than u did

[@jcers]

I love trig identities way too much lol

[@muzyarw]

at 4:33 why did you write 1 - sin theta at the denominator?

[@jeminmangukiya8655]

hi Brian I am from India I wanted to know wheather this part of precalculas is of college level or is it of high school

[@brianmclogan]

this is apart of my pre-calculus class

[@abhirajarora7631]

True for all theta, except when sin theta becomes zero or one.

[@andrearamos1243]

Super helpful ❤

[@spencerblanchard480]

Why is your green cap on the black marker and the black cap on the green marker?

[@tina-iv7gr]

In the second step, how did you go from cot to cos/sin?

[@brianmclogan]

+Tacina Howard quotient properties