Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent

Oh man, what is all this sine and cosine business? What do these things even mean?! And Greek letters now? I don't know Greek! OK friend, just relax. Understanding the trig functions is as easy as pi radians. We just make some triangles and set up a few definitions. I promise it's no sweat, just watch this!
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[@ProfessorDaveExplains]

Yikes, it looks like I accidentally used numbers for the side lengths in the checking comprehension that don't abide by the Pythagorean Theorem! How embarrassing. Luckily it doesn't really change what you're doing, but my apologies for this ridiculous error anyway.

[@williamadams137]

Professor Dave Explains use a 5 12 13 triangle

[@helenday5031]

ProfDave. I didn't actually notice, as I'm not that knowledgeable yet on Pythag triangles. And others users of this site may feel the same as me, ie, so grateful for your marvellous lessons that the odd , small normal human flaw is entirely forgiveable and doesn't matter.

[@pinklady7184]

That must mean your brain was overworked and thereby your concentration dropped.

[@asharalam12]

@@williamadams137 hr

[@asharalam12]

Yehuh. Help. Hei Sjisjuvjbdhhbd buns Snhsheienzken! Silbsj Nsjs.ksnj Bsmje Ndjjsnssmms Jmshsj Snsmsjsks Jss.hs Shs Zis Ssksjsnss Kss Snssnnsjsjs Msnsnnsndhdhhdhdhdhbx Jdjjsnsjsjjsjsjsjjx d Njxjdnsjsnjdjsjsm x k Dxj.djjnnnn

[@jimjohnston6848]

I really love the approach you take to working with these concepts. I have been running away from any form of math for over 50 years, but, now, thanks to your vids, things are making sense, and I am really enjoying spending time taking notes and solving problems.

[@bpgmemes1813]

that's really cool

[@KeepFightingStruggler]

Wow man, great job and keep it up

[@hassannur3763]

when I mostly needed it thanks Jesus

[@Ahmed-ii7up]

No, thanks, professor Dave.

[@majesticdoge1163]

No, thanks, Cr1tikal

[@vertiigo.]

No,thanks,One God and dave

[@jeremylemans3005]

No, thans Soh Cahtoa

[@allansayed5633]

I am going down a rabbit hole; I started from cellular membrane potentials to electricity to electron fields to the electrodynamics to the quantum mechanical definition of energy to chemical bond energy to atomic orbitals to Schrodinger's equation to trigonometry. The moment I heard "SOHCAHTOA" brought back a flash of highschool physics classes. I wish i paid attention in highschool.

[@alexbellury]

Haha same I'm going back over high school math since at least in the US the foundation we build on is so poor. I finished Calc 2 and was about to go into linear algebra but I've decided to go back and fill in the gaps that have held me back. Good luck on your journey! I'd be interested to see what you're learning now.

[@larryzhang8557]

@@alexbellury Same here. Going over calculus and linear algebra for studying machine learning. Trig is the thing that really holds me back. Good luck guys. (I laughed instantly and knew what he is about to say when I saw "rabbit hole", lol)

[@rihyanny]

​@@larryzhang8557Hello there, sorry for replying to you comment I have no choice but to since you're the only one with a recent comment. I was wondering if you can explain to me how did they evalutae the 60° angle at 5:10 I somehow did not understand, sorry🥲.

[@justanotherday123]

it's not too late to go back to school brother

[@robertmauck4975]

​@rihyanny so, for the 60° angle calculation, you use the 30-60-90 triangle, but start from the 60° angle instead of the 30° angle. Since we are looking at the triangle from the other angle, what was adjacent for the 30° calculation is now opposite, and what was opposite is now adjacent. I hope this helps

[@HellooDae]

I took a look at your channel, and I have lots of respect for you. Multiple playlists about different subjects, and all of such high quality. I watch this videos everyday, because I dream to just be good at math, and there is already a lot of improvement. I have been watching since December, it is March now. Thank you, from the bottom of my heart.

[@jagruti_rs]

Prof owe you!! No other like you or somewhat near to be like you.. have ever came up! ❤️

[@Wintersghost135]

When I was in college, I used to joke that I’d name my daughter SOHCAHTOA and my son IUPAC. You’re a chem guy so you’ll get that. Yeah, I love it that much.

[@georgesadler7830]

Professor Dave ,thank you for a short and outstanding video on Trigonometric Functions. These classical Trig functions are the heart and soul of Trigonometry.

[@eeliot2961]

God, I hate trigonometry. This was helpful though

[@INVALIDZEROTheTitSucker69]

Why? This is fun

[@Siduch.]

@@INVALIDZEROTheTitSucker69 🤓

[@thatomofolo452]

😮

[@_Zh4dow_]

​​@@Siduch.W?dym trigonometry makes me twerk 73 times per second

[@Israa0000]

​@@_Zh4dow_literally omg 😭😭😭 trig 🔛🔝

[@هایدهنرماشیری]

My sincere gratitude to you, professor Dave.❤

[@yarawaleedesmail3886]

Thank you so much professor, really that helped me alot

[@defacube]

I didn't think I would learn 6 trigonometric functions from a 7 minute youtube video. This was really helpful

[@lelouchvibritanniacommands5211]

Thank you very much! Finally, I understand something after one semester of no understanding

[@smj5785]

Same 😂

[@quiruzjamesallenf.6578]

Same

[@DevDevi]

Wow, this was some seriously good explaining.

[@rubenb8653]

The title Prof. and the into were enough for me to sub hahaha. (I'm a C programmer btw, but my terrible past in school made me have to go back to this stuff haha. Life's weird.)

[@whenthethebeansstrikeback6728]

I see you're a man of Memory Allocation as well

[@gurkirpasarao2072]

GOD THANK YOU FOR THIS GUY !!!!!!!!

[@notsosmart3288]

man he is jesus afterall

[@MiltosPol-qn3zh]

I was waiting for these certain tutorials for four months!!!!

[@ProfessorDaveExplains]

patience pays!

[@yajatyadav3348]

Hi Professor Dave, I wanted to ask if these functions for all triangles or only for right triangles(because you mention hypotenuse). If they only work in right triangles, in the comprehension check, you listed a triangle with legs 8 and 3 which wouldn't have a hypotenuse of 11.

[@ProfessorDaveExplains]

Yikes what an error! Put that on my list of most egregious mistakes.

[@zainmustafa090]

the best teacher on the internet

[@aleksszukovskis2074]

3blue1brown is a great alternative too

[@AnamshaAnsariAnamshaAnsari]

Your explanation is truely excellent... It clear so much concept of my Trigonometry..

[@chrisnl7354]

I learned more in 7 minutes than my teacher taught me in a month

[@Zxter]

I feel like a genius after learning “SOHCAHTOA”

[@ended-randomcreations]

i can't believe im using this for minecraft...

[@drproton85]

Thank you, thank you, thank you, thank you, THANK YOU! Jeez been stuck on college precal on this. I'm like, "WTF IS SINE!" The book we were provided didn't have the SOHCAHTOA abbreviation. That's so awesome!

[@clashofroyaleclans9592]

I am also so thankful for this video. This really helped me for my seventh grade exam!

[@RandomGoldieStuff]

You sir are single handedly saving my butt this semester

[@alameenahmed212]

From the best KZbin teachers

[@legendrams548]

Subscribed, very good graphics and explanation 👍

[@RainMoneyProductions]

thank you so much. I cant tell you how much easier this made my life

[@joelgerlach9406]

@Professor Dave Explains I just wanna mention that the triangle at 6:19 wouldn't even be a triangle since 8+3=11, meaning the triangle would be a line..

[@ismailhaggar7429]

All the respect to you, Sir ❤

[@aminmkyt4191]

I've been living in cyprus for less than 2 years and my greek is not so good, so I can't understand the trigonometry easily but THIS guy can help me learn it on my second language Which os english(yeah I'm flexing) and translate them into greek So thank you legend

[@shinoahiragi7624]

what's ur first language ?

[@yamatanoorochi3149]

Some Old Horses Can Always Hear Their Owners Arrive

[@maisasaza6848]

legendary. thank u so much. i skipped this in high school

[@Realgoldenspringy]

Thank god I can watch a quick review before my math final today

[@ccuny1]

Great tutorial (addendum corrects errors so no biggie). May I ask what you used to animate starting at 0:25? It's neat and clear.

[@ProfessorDaveExplains]

adobe after effects!

[@ccuny1]

@@ProfessorDaveExplains Nice work. Thanks a lot.

[@manobrodeful]

"The sine of theta" sounds like an Elder Scrolls quest

[@MajedSalmaoun]

you are a legend bro All Love For You

[@syamkumartelakarapu8186]

Wow. My self surrendered to this explanation

[@thobilemasoka6655]

Thank you so much sir, this was really helpful ❤️❤️🙏

[@AlessandroZir]

u r just fantastic!! youtube justified its existence with you;

[@TomAustinIII]

Dave, you're awesome!!!

[@anarchohannibalism]

who else is cramming for trig the night before their final exam 🙋

[@anthonystark6215]

Thank you, Professor!

[@stevkohudran]

Thank you, I can understand math better at school now!

[@manuelmarrujo8197]

Thanks. You saved the day

[@shade7158]

0:12 Hollow knight jump scare.

[@ruleroftime]

i hope youve had a good two months to thoroughly reflect on what youve just said and why it isnt funny

[@shade7158]

@@ruleroftimeI don’t really mind, I wasn’t really wanting to draw attention it was more like a note for myself. If you think it’s unfunny then I respect that and good for you.

[@shade7158]

@@ruleroftimeAlso I mean no harm but remember to use punctuation when typing you’ve.

[@medamness]

It help me a lot, thanks

[@kuldeepbadhan781]

Thank you so much sir for this valuable content that you are providing for free. May god bless you 😊.

[@vicentpen1656]

Dave is a admirable educator.Always give us high quality Instructional video.And all of them are free.Bless him.

[@Philomena-qs8qd]

Thank you ❤😊

[@LIANZESOH]

what is the purpose for having a reciprocal of original trigonometric functions if it is basically just reversing the position of lengths in the ratio?

[@MrMannyWolf]

Still clueless, but I did jam a melody to the music at the end. Win!

[@crazyjester993]

3:37 don't get confused between substitution a=a and a=b

[@nousheenrashid6923]

1. Some People Have = Sin0=Prependicular/hypotenuse 2. Curly Brown Hair =Cos0=base/hypotenuse 3.Tidy Pant Bushet=Tan0=prependicular/base

[@BaccaratDegen]

After much practice I totally get it

[@jhonmarkromero1891]

Thanks a lot Prof Dave🙏

[@porky1118]

I just memoize the most important results to remember, which ratio is sin/cos/tan

[@neonknowledgehub9172]

1

[@HarrySia]

thank you math Jesus

[@neillu]

An 8-11-3 right triangle?!😂

[@ProfessorDaveExplains]

argh i know, one of the dumbest errors in the history of the channel!

[@redangrybird7564]

@@ProfessorDaveExplains I think you can re-upload a corrected version of the video in the same video place and don't loose "likes".

[@ProfessorDaveExplains]

unfortunately you can't :( otherwise there are about a dozen videos i would have updated a long time ago

[@redangrybird7564]

@@ProfessorDaveExplains so, if you re-upload you loose the likes? Or definitely you can't re-upload in the same place? I have seen other channels re-upload newer or corrected versions of their videos. Anyways, good videos, I have learnt heaps. Thanks. Take care ✌😷

[@pinklady7184]

I was looking at that too.

[@SV-cb6iy]

Amazing tutorial!

[@Shailendrap008]

Prof i love your chanal so much i considered subscribing

[@AlessandroZir]

thank you very much!❤❤❤

[@thewierdragonbaby4843]

In the hyperbolic functions video, you explained that sinh x = e to the x - e to the -x all over 2. Is there a formula like this for the regular sine (or any of the other functions for that matter)?

[@carultch]

The answer is yes. And it involves imaginary exponents, and imaginary coefficients in the case of sine. Cosine is the easiest to remember in this form, and knowing that cos(x) = d/dx sin(x), you can derive what sine(x) needs to be in terms of the natural exponential. sin(x) = (i*e^(-i*x) - i*e^(i*x))/2 cos(x) = (e^(i*x) - e^(-i*x))/2 You can see the parallels to sinh(x) and cosh(x), because: sin(x) = -i*sinh(i*x) cos(x) = cosh(i*x)

[@thewierdragonbaby4843]

@@carultch Thanks for the reply. Back when I wrote this comment I understood what imaginary numbers where but struggled to find a formula for sine anywhere on the internet and this would've really helped. Although I actually found a video on it in the meantime and if I had remembered I would've deleted this comment but I forgot. Thanks for the reply anyway

[@Dragon_Ball_super_75]

Thanks professor

[@pokerlover1662]

Hi, I have a question; @4:44 for the 30-60-90 triangle why is one side square root 3. I understand it's a rule but what's the reason or method of finding that? (I didn't see the geometry videos)

[@alexanderjuzelac]

I am just here because I need more info on the tan, sin, cos, cot, csc, sec, floor, and ceiling, blocks in scratch and yet here I am, a 12 year old at 8:54 learning trigonometric functions. I also have a B in math.

[@___pollene2534]

ur a life saver

[@matokurin]

Thanking you.

[@Krageon-Offline]

Ifsec(x)cos(x)=sin(x), how does sec(π/2)cos(π/2)=sin(π/2)=1?

[@sewaraldahab1588]

thanks for the video!

[@sachindks]

thank you sir

[@NieLL1]

SOHCAHTOA reminds me of HAWK TUAH for some reason

[@zhabelbaya1169]

Thank u🥹

[@-0-__-0-]

I was looking for this topic for my game engine and look who I found, its Chemistry Jesus ☺️. Thank you Chemistry Jesus

[@frozengaming4459]

Amazing No words to describe you Love from India❤️

[@jerrymiaharelee6040]

i dont get its since my teacher puts x and a number and you dont know what the length of the other side and he gets x= 3/2 and y= radical 2/2

[@KevinTempelx]

Thanks!

[@vashtv127]

I want to learn this to impress my class

[@educationalpurposes2156]

Wow! Thanks!

[@vjysharnan]

Hello Dave I'm vijay from India...sohcahtoa is top notch.

[@carultch]

सीन: ओपपसिट ओवर हीपाटेनूस कोसीन: आझैसेनट ओवर हीपाटेनूस टानजनट: ओपपसिट ओवर आझैसेनट

[@ferdiemanalac7814]

Sir where did square root of 3 come from

[@carultch]

The 30-60-90 right triangle is a special right triangle, that is exactly half of an equilateral triangle. Start with an equilateral triangle,, with the bottom side horizontal, and all side lengths equal to 1. Label the corners, A, B, and C, proceeding counterclockwise from the right point. Now split the line AC in half, and call the midpoint D. We now have a right triangle, A, B, D. The angles of all sides of an equilateral triangle is 60 degrees, and since the angle at point A remained unchanged, its angle is 60 degrees. The angle at point B was cut in half, so it is now 30 degrees. The angle at D is a right angle. We know side length AB, which is the original side length of the equilateral triangle, which of course is 1. We also know side length AD, because it is exactly half of AC, which was 1. Therefore we know side length AD to equal 1/2. Set up lengths AB, AD, and BD in the Pythagorean theorem. AD^2 + BD^2 = AB^2 Solve for BD: BD = sqrt(AB^2 - AD^2) Plug in AB = 2 and AD = 1 BD = sqrt(1^2 - (1/2)^2) BD = sqrt((2/2)^2 - (1/2)^2) BD = sqrt(4/4 - 1/4) BD = sqrt(3/4) BD = sqrt(3)/2 We now show that triangle A, B, D has leg 1 equal to 1/2, leg 2 equal to sqrt(3)/2, and a hypotenuse of 1.

[@emmylouhaught8572]

Wish there is acronym for the other 3

[@Jose-jh4xb]

thank you math jesus

[@smj5785]

S O H C A H T O A 🤝🏻

[@sreejishapk8023]

This video more usefulness 👍👍

[@tarunarachmad3976]

4:35 As we recall from geometry

[@aashrithakella-u5d]

this helped me with my maps test lol

[@gregfat1432]

Very good

[@HarlowAnders]

God, I love trigonometry. This was helpful though

[@tGoldenPhoenix]

thank you

[@tGoldenPhoenix]

Done.

[@jyothieswar5575]

if theta is an angle in right angle triangle it should be compulsorily acute angle then why we care about 2,3,4 quadrants please respond

[@ProfessorDaveExplains]

Because the triangle itself is located in those quadrants. Start the trigonometry playlist from the beginning, it explains the stuff you need before this one.

[@jg6551]

thanks

[@SV-cb6iy]

Professor, which app do you use? Thanks

[@dabo6758]

Hello, but 8,3 and 11 is not a Pythagorean triple 😇

[@Mahad12ml]

What grade maths is this in the US ?

[@lenyfreeman3807]

You lost me at 5:20. I don't understand why we use root 3 on the adjacent leg.

[@ceegae1670]

He was talking about the 60° angle, which is at the top. I think you were looking at the 30° angle which is why that looked weird

[@Muntasir1023]

Thank u so much...u

[@FreshBeatles]

You're wrong at: 5:00 the 30 60 90 triangle doesnt have a hypotenuse of 2, it has a hypotenuse of 1. It has a hyp of 1 because it is the radius line of the unit circle. Trust me, if you draw your own triangle within the unit circle for 30*, you can see that the adjacent (x) is Clearly sqrt(3) / 2. Likewise, you can simply use the pythagorean theorem to get 1/2 for the opposite, even better, you can plug in sqrt3/2 into X for the equation: x^2 + y^2 = 1 since that is the equation of the unit circle; and youll end up with 1/2. The coordinate point should be (sqrt3/2 , 1/2) , however, in your illustration at 5:00, your triangle has different sidelengths, and the point would actually be at (sqrt3, 1) for your explanation.

[@ProfessorDaveExplains]

The hypotenuse is not the radius of the unit circle. It's just a triangle. And those are its dimensions. What a bizarre comment.

[@Quran.And.Science]

Good

[@TitanTubs]

A month of maths in 1 video

[@glasssmirror2314]

Hi sir Yr abbreviations @ 1:17 are confusing.U mentioned Sec for Cosine while Sec is for Sine. To avoid confusion pls use standard abbreviations as follows Sin Sec Cos Cosec Tan Cot

[@ProfessorDaveExplains]

I'm not sure what you're talking about, csc is the abbreviation for cosecant, they are correct as shown.

[@glasssmirror2314]

Hi Prof Dave Tks Prof as @ 1:17 these abrvs are aligned but then realised they are reciprocals.