Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent
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- Опубликовано: 21 авг 2024
- 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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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.
Professor Dave Explains use a 5 12 13 triangle
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.
That must mean your brain was overworked and thereby your concentration dropped.
@@williamadams137 hr
Yehuh. Help. Hei
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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.
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.
@@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)
@@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🥲.
when I mostly needed it
thanks Jesus
No, thanks, professor Dave.
No, thanks, Cr1tikal
No,thanks,One God and dave
No, thans Soh Cahtoa
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.
that's really cool
Wow man, great job and keep it up
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.
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.
Prof owe you!!
No other like you or somewhat near to be like you.. have ever came up! ❤️
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.)
I see you're a man of Memory Allocation as well
Professor Dave ,thank you for a short and outstanding video on Trigonometric Functions. These classical Trig functions are the heart and soul of Trigonometry.
God, I hate trigonometry. This was helpful though
Why? This is fun
@@INVALIDZEROTheTitSucker69 🤓
😮
@@Siduch.W?dym trigonometry makes me twerk 73 times per second
@@_Zh4dow_literally omg 😭😭😭 trig 🔛🔝
I didn't think I would learn 6 trigonometric functions from a 7 minute youtube video. This was really helpful
Thank you very much! Finally, I understand something after one semester of no understanding
Same 😂
Same
i can't believe im using this for minecraft...
My sincere gratitude to you, professor Dave.❤
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.
Yikes what an error! Put that on my list of most egregious mistakes.
the best teacher on the internet
3blue1brown is a great alternative too
I was waiting for these certain tutorials for four months!!!!
patience pays!
I feel like a genius after learning “SOHCAHTOA”
Wow, this was some seriously good explaining.
GOD THANK YOU FOR THIS GUY !!!!!!!!
man he is jesus afterall
Thank you so much professor, really that helped me alot
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!
I am also so thankful for this video. This really helped me for my seventh grade exam!
I learned more in 7 minutes than my teacher taught me in a month
From the best RUclips teachers
Some Old Horses Can Always Hear Their Owners Arrive
i finally get it! so fun! thanks!
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
what's ur first language ?
You sir are single handedly saving my butt this semester
Your explanation is truely excellent... It clear so much concept of my Trigonometry..
@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..
Subscribed, very good graphics and explanation 👍
1. Some People Have = Sin0=Prependicular/hypotenuse
2. Curly Brown Hair =Cos0=base/hypotenuse
3.Tidy Pant Bushet=Tan0=prependicular/base
3:37 don't get confused between substitution a=a and a=b
All the respect to you, Sir
❤
thank you so much. I cant tell you how much easier this made my life
"The sine of theta" sounds like an Elder Scrolls quest
Wow. My self surrendered to this explanation
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.
adobe after effects!
@@ProfessorDaveExplains Nice work. Thanks a lot.
Dave, you're awesome!!!
Thank god I can watch a quick review before my math final today
who else is cramming for trig the night before their final exam 🙋
I just memoize the most important results to remember, which ratio is sin/cos/tan
1
Thank you so much sir, this was really helpful ❤️❤️🙏
thank you math Jesus
Still clueless, but I did jam a melody to the music at the end. Win!
Thank you, Professor!
Thank you so much sir for this valuable content that you are providing for free. May god bless you 😊.
Dave is a admirable educator.Always give us high quality Instructional video.And all of them are free.Bless him.
you are a legend bro All Love For You
Amazing tutorial!
Thanks a lot Prof Dave🙏
An 8-11-3 right triangle?!😂
argh i know, one of the dumbest errors in the history of the channel!
@@ProfessorDaveExplains I think you can re-upload a corrected version of the video in the same video place and don't loose "likes".
unfortunately you can't :( otherwise there are about a dozen videos i would have updated a long time ago
@@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 ✌😷
I was looking at that too.
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.
u r just fantastic!! youtube justified its existence with you;
Thank you, I can understand math better at school now!
Amazing
No words to describe you
Love from India❤️
It help me a lot, thanks
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?
S O H C A H T O A 🤝🏻
Thanks. You saved the day
Thank you ❤😊
After much practice I totally get it
I want to learn this to impress my class
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)?
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)
@@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
thanks for the video!
4:35 As we recall from geometry
Ifsec(x)cos(x)=sin(x), how does sec(π/2)cos(π/2)=sin(π/2)=1?
Prof i love your chanal so much i considered subscribing
Thanks professor
thank you math jesus
thank you very much!❤❤❤
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)
You lost me at 5:20. I don't understand why we use root 3 on the adjacent leg.
ur a life saver
I was looking for this topic for my game engine and look who I found, its Chemistry Jesus ☺️. Thank you Chemistry Jesus
Thanking you.
Wish there is acronym for the other 3
thank you sir
Thanks!
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
Hello Dave I'm vijay from India...sohcahtoa is top notch.
सीन: ओपपसिट ओवर हीपाटेनूस
कोसीन: आझैसेनट ओवर हीपाटेनूस
टानजनट: ओपपसिट ओवर आझैसेनट
Wow! Thanks!
Thank u🥹
Sir where did square root of 3 come from
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.
God, I love trigonometry. This was helpful though
Very good
thank you
Done.
thanks
I’m confused, you didn’t derive any of the functions, you just stated them.
A month of maths in 1 video
PBP
HHB
Hello, but 8,3 and 11 is not a Pythagorean triple 😇
This video more usefulness 👍👍
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
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.
thank you charlie white
Good
Professor, which app do you use? Thanks
6:23 cannot be a triangle @Professor Dave Explains
yeah that's my bad
6:35 Are you joke? A triangle with sides 3, 8, 11 does not exist!
Yeah check the pinned comment, this is a candidate for the dumbest mistake on my entire channel.
Thank u so much...u
Thanks Jesus