Trigonometry full course for Beginners
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- Опубліковано 12 чер 2024
- Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of #triangles. Throughout history, #trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities, which are equations used for rewriting #trigonometrical expressions to solve equations, to find a more useful expression, or to discover new relationships.
In this trigonometry full course you will learn everything of trigonometry in details. The following topics of trigonometry have been discussed in this course.
⭐️ Table of Contents ⭐
(0:00) Angles
(26:32) Right triangle Trigonometry
(53:03) Law of Sines
(1:14:10) Law of Cosines
(1:30:22) Points on a circle
(2:00:47) Others trigonometry functions
(2:17:19) Graphs of sinx and cosx
(2:50:00) Graphs of tan, cot, sec
(3:13:17) Invers trigonometric function
(3:33:39) Solve trig equations
(3:53:49) Modeling with trigonometry
(4:11:10) Solve trig equations with identities
(4:30:58) Finding new identities
(5:03:18) More identities
(5:24:56) Using identities
(5:57:59) Finding new identities
(6:10:20) More identities
(6:31:51) Review trigonometry function
(6:53:53) Riview trig proofs
(7:08:03) Polar coordinates
(7:34:56) Polar form of complex numbers
(7:57:25) DeMivre's theorem
(8:15:18) Sequences
(8:35:23) Series
(8:52:00) Arithmetic Series
(9:10:26) Geometric Series
(9:26:18) Mathematical induction
⭐️ Credit ⭐
Author: Tyler Wallace
License: Creative Commons Attribution license (reuse allowed)
Website: / wallacemath
⭐️ Join Us ⭐️
Join our FB Group: / cslesson
Like our FB Page: / cslesson
Website: cslesson.org
⭐️ Table of Contents ⭐
(0:00) Angles
(26:32) Right triangle Trigonometry
(53:03) Law of Sines
(1:14:10) Law of Cosines
(1:30:22) Points on a circle
(2:00:47) Others trigonometry functions
(2:17:19) Graphs of sinx and cosx
(2:50:00) Graphs of tan, cot, sec
(3:13:17) Invers trigonometric function
(3:33:39) Solve trig equations
(3:53:49) Modeling with trigonometry
(4:11:10) Solve trig equations with identities
(4:30:58) Finding new identities
(5:03:18) More identities
(5:24:56) Using identities
(5:57:59) Finding new identities
(6:10:20) More identities
(6:31:51) Review trigonometry function
(6:53:53) Riview trig proofs
(7:08:03) Polar coordinates
(7:34:56) Polar form of complex numbers
(7:57:25) DeMivre's theorem
(8:15:18) Sequences
(8:35:23) Series
(8:52:00) Arithmetic Series
(9:10:26) Geometric Series
(9:26:18) Mathematical induction
Thank you for the time stamps and for sharing your expertise.
My man you are a legend
hey i am in tenth class. will this be understandable for me?? or am i just wasting time (plz dont take in a negetive sense. i am so weak in trigonometry so i have to learn for knowledge sp plz reply)
@@yashchaturvedi864 i think ya..also u should give it a try..
Whoa 😮 🙀
9 hours ago I was a square, now I'm a triangle.
🙏
I am a curve under a graph
@@amadeus7511 How?
@@fuji_films dunno
@@amadeus7511 the area under a curve on a graph?
learning math is so much easier with this video, in my air conditioned house, with a whole table for my notes, with the ability to pause and rewind, at my own pace, with no distractions, than it was as a teenager in a classroom. big thanks
It's so much easier than any online course I've taken.
Bro could u please tell me for which class he is telling .
Currently I am in 12 preparing for jee is it helpful to me
@@meerasaivasamsetti5145 What do you mean?
@@sacrific1al00 heya! I was asking is this helpful for my jee preparation
Jee is Indian entrances exam for IIT
@@meerasaivasamsetti5145 Sure, it will be helpful.
I was failing math. You taught me what my teacher couldn't in a whole year, in 9 hours. Thank you so much, I am so grateful that you provided your amazing teaching for free on youtube.
same fam same
@@wirelessmoke tbh i feel bad for not always having the balls to really do those hard stuff, like learning things like this one....
i just wanted to change...
Be GREATFUL TO ALLAH, WHO HAS CREATED HIM ❤️
he is overqualified to be a teacher
props to the creator for having the patience of going through all of trigonometry
Can we just take a moment appreciate that this video has no ads
theres a few ads on mine, would gladly go through it though for his hardwork
well there are ads for me , but idc he should deserve for his hardwork
You shouldn’t have ads if your account has some specific settings on
Because i use adblock. I forgot what ads are with this blocker.
I have ad blocker in UA-cam
If by any chance, quantity of scientists increase in 21st century, your contribution will be incredibly significant...👍
omg 👀
@einstein come check this bro
I agree
I wouldn't say so, but he's not bad.
Come to India you will find many there who have this whole video learnt. Cuz we have this while thing in our 11th grade.
You literally deserve an award for saving life of millions of students!!
1.1 million
Literally. Saving Lives. I don't think you know what literally means. And I mean that... literally.
i’ve spent 2 years trying to understand trigonometry and now i achieved my goals in 9 hours. it’s amazing to see that people like you are real life superheroes. If any great mathematical achievement, the cure to cancer or ageing, or space travel comes you can know and rest assuredly that it was, in some part, your contribution. Thank you and keep up the amazing work
Am I dreaming or I just found a youtube channel that posted tutorial videos each 8-9 hours long in every subjects that will benefits a lot of people and students? 😮
Hlo madam
It's a dream come true 😳
The circle in radians has always looked like magic to me and about 25 years after graduating from high school, this video has finally solved the mystery while sitting in the comfort of my home. I am indeed very grateful to the tutor in this video. I've only completed the first chapter and I intend to watch the entire 9 hours plus. And one more thing..., am really eager to support the maker of this video. Please how do I do that? Thanks in advance
This is really good I'm studying it right now and It's fun to do this
Ahh yes the “Angle of Depression” , I think I know that one too well lol
Bro may be everyone know this angle very well those who watching this vdo😂😂
Trigonometry = Algebra + Triangles + Circles + Degrees, I love it.
where is the algebra? asking as a learner
oh for conversion?
God is coming soon to judge the world! ✝️
@@SATISFYPLANET shut up its a math video
@@SATISFYPLANET 👹 nope
The Best teaching I have seen on this subject very well done, cheers.
Oh my good, this is soooo perfect, this is sooo neat, the topics you picked, their order, your idea of asking a leading question at the beginning of every chapter, the way you use multiple colors, the way you draw the figures, even the way you SPEAK, even your voice makes this sooo relaxing, everything is perfect, i'm lucky to find this video. It took you 10 hour, and maybe even more if we count editing and fixing, but it did worth it, we all appreciate your labor!!! i'll watch graph theory and calculus later, please keep going!!!
TRUE
its so fun going back and refresh the lessons from HS
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not until u encounter new things in trig that your school havent teach u. this video deserves more
0:00 Angles ✔️
26:32 Right triangle Trigonometry ✔️
53:03 Law of Sines ✔️
1:14:10 Law of Cosines ✔️
1:30:22 Points on a circle ✔️
2:00:47 Others trigonometry functions ✔️
2:17:19 Graphs of sinx and cosx ✔️
2:50:00 Graphs of tan, cot, sec ✔️
3:13:17 Invers trigonometric function ✔️
3:33:39 Solve trig equations ✔️
3:53:49 Modeling with trigonometry ✔️
4:11:10 Solve trig equations with identities ✔️
4:30:58 Finding new identities ❌
did you continue after that ?
Sin(30)⅓+cos(78)⅔=?
I really like this course because he goes step by step and provides you with lots of examples, making a seemingly giant monster of a course seem like a puny bacteria
My math class doesn’t go this deep into trigonometry. Thank you
So far in the first 5 minutes, I am convinced that prepping for my Pre-calculus subject will be worthwhile. Thanks for this informative video.
Day 1: Fully completed Angles section - Difficulty: easy, but took effort to understand. (26:32) - 14/02/2021
Day 2: Completed Right Angle Trigonometry until (53:03) - 15/02/2021 - I learned functions of SOHCAHTOA; how to find out angles and triangle sides. - Difficulty: easy, it was so coooooool ☺︎
Day 3: finished Law of Sines (1:14:05) - Difficulty: easy but really cool! 16/02/21
Day 4: finished Law of Cosines (1:30:23) - Just amazing thank you so much! 17/02/21
Day 5: studied a little bit about right and not right angle triangles, but didn't watch the video. 18/02/21
Day 6: (FINISHING STUDYING TRIG) - Finished the Points on a circle (2:00:48) - 19/02/2021
Hey guys just wanted to tell you something: i am 12 years old, it was easy for me - i watched till 2:00:48 - but i'll stop now because it's enough math i know now to study a book i bought on Physics (the name is Physics for Dummies). If you are older than me, i'm sure you will understand it much easier, this professor is just amazing, thank you so much.
it's great to hear from you, i hope you can help your friends too!
I am 16yo and I don't know nothing about trigonometry, should I star from this video?
@@andresantiago1175 yeah! I was scared at first because the problems and stuff looked hard, but it's really easy actually. You'll do fine :)
Ahh I wish I had started that early studying math/physics. Good luck on your journey btw.
@@A5A5A5A5h thanks :) Yeah I have a big interest in those topics I hope I can become a physicist some day :))
7:51:00 So he actaully did a shortcut here but I want to elaborate how you can get that answer step by step:
1. Since a and b are constants, you can separate them from the rest of the equation.
2. Multiply the equation by the conjugate of cosB + isinB (which is cosB - isinB)
3. On the top you will get (cosB - isinB)(cosA + isinA) and on the bottom you should get cos^2B + sin^2B, which you should know equals 1
4. Foil out the top and you should get (cosAcosB + sinAsinB) + (cosBisinA - cosAisinB)
5. Factor out an i in the second term. This will give you i(cosBsinA - cosAsinB)
6. From the sum and difference identities, you should get cos(A - B) for the first term and sin(A - B) * i (or just isin(A - B) for the second term.
7. Add the together and tack on the (a/b) to get your answer: (a/b) * [cos(A - B) + isin(A - B)]
This is very helpful. Thank you.
Thanks, I'll use this to help when I get to that part 👁U👁👍🏾
May God Bless You
I love the way his English is so Fluent!!! I'm from BANGLADESH 🇧🇩
But still I'm watching it just because I like his English
YES!! I've finished the video! :D I copied the most important things in my notebook and now I need to practice, then continue to the next step
Im so happy
every single person at 1:02:19 be like: *intense chuckling
🤣🤣
*Hardcore laughing
I was really wishing he would say it just for the joke XD
I am so thankful for this video! I am currently a physics major(freshman) and I recently switched to online instruction due to my father's health, and so with everything going on, I felt like I was dumb and got imposter syndrome. This video has changed my life because it gave me back the confidence I needed. Thank you, Khan academy, for being such an amazing resource!
THis has helped me understand more clearly and I'm able to follow my instructor during his lectures. Thank you :)
One of the best online courses! Thank you for the thorough, fine work!
i am asking people what is triagnometry and what are its usage since 2015. but the all were failed making me understand it. but by just watching this video for 50 minutes, you cleared my mind on its very essential basics.
Man you make mathematics so easy. What I like more in the way you teach, is how easy you relate concepts together, and that makes a huge contribution to knowledge. You are a superman 🦾🦾🦾. Thank you so much!!!
Best video ever I have seen on trigonometry
Finish the entire course 💪💪 It's time for doing some exercise
legend not gonna lie.keep up the goooooooodo work
My geometry class has been going pretty slow, and we’re nearing the end of the year.
This is the best video to be recommended by UA-cam to me I swear-
I may be learning this really early, but I don’t care, it’s fun!
This video has helped me a lot as a maths teacher. The explanation is very cohesive and clear. Thank you very much for this.
It's my first to understand trigonometry at this level and at this standard of your teaching , l know how to deal with this topic. Thank you so much may God bless you
This is exactly what I’ve been looking for. My highest math was Algebra 2. However, I had statistics in university. What’s sad is that I really wanted to advance myself, but no one really showed me how. So unfortunately, I followed with the curriculum flow, but that’s in the US. In Japan and South Korea, EVERYONE takes the same courses, regardless of level. At least these countries do this better than the US, along with cars, airlines, and airports.
Man , you are truly a genius , everything is explained in simple and easy way
Thank you, I love you for this
Blessings and love to you and those you love
Let's take a moment to acknowledge the skill of this guy as a teacher. I wish our colleges were filled with teachers like him.
Mastery of the basics is the key to mathematics... and this video is an perfect example of the mastery of the basics of trigonometry. Thank-you so much!
Re-learning TRIG to strengthen my chances in upper level mathematics!! Calc 2 HERE I COME!!!
Personal Bookmarks:
1:40:58
2:17:20
2:44:29
3:13:17
3:36:52
4:01:54
Really I was so curious to learn trigonometry but I was looking up for a perfect teacher and that was u
Thank you to you and all these special people who took the time to share their knowledge gracefully, asking nothing in return!
Thanks man. I am an undergraduate student but still didnt understand high school trignometry until i saw this video. You are a great teacher
Fantastic. Very clear and easy to understand. Thank you.
He is the perfect definition of angel!
15:23 there is an easy method to convert angle into radians
We have to multiply that angle into 180/π
Thank you for sharing this lesson, it is decent and useful.
Man, this helped me a lot. I am forever grateful, I hope one day I can become a great teacher as you are.
Great course. Thank you so much for this.
1:40:00 i also noticed a thing that i'd like to share..(Consider r = pi) that is at 120 degree 2r/3 , so if we keep the same denominator and numerator we do (2+3)r we get 5r/3 witch is opposite of 300 degrees value, so if we follow the pattern for 1st quadrants, we get 3rd quadrants and for 2nd quadrants, we get 4th quadrants.
5:02:35 I believe should be cosv - cosu so you would have to multiple by negative 2 to get cosu - cosv = -2sin((u+v)/2) * sin((u-v)/2)
its really great for the learners
This videos length proofs that it's made with pure dedication
amazing!! I speak spanish and I can understand u perfectly
I'm trying my luck here as I can't understand trigonometry in my native language.If I can't understand it here, I will try my luck on German math channels.
How appreciatable that many of the teachers were not able to teach us as good as he did
Thanks a Bunch!!
2:12:41 important unit theorem sec and cosecs are the reciprocal of their corresponding cos and sin plus do make sure to rationalize the trignometric ratios in the reciprocals
2:17:19
If there were many people like u the world will be changed into more civilization.thank u so much dear!
Exactly my thought these online educators like this brilliant professor are changing thousand of lives showing students not give and pursue their careers and their dreams. It is every inspiring. Nothing is impossible to learn actually it turns out to be fun and challenging than wasting our times on social media. There are a lot of people who want to be in our place and get this stuff for free. We are blessed. May God bless this channel and the people who work so hard to being this incredible content for us.
43:07 the triangle on the right is an isosceles triangle, so you could solve for the missing side of the triangle on the left and you would have your x
whoever made this video, i love you
Thanking you forever wouldn't be enough🦾
On the last part of problem 3 at 45:00, I just used substitution to solve for Z =(x+y) instead and then subtracted y from z to get X. Way simpler than all that cross multiplying and parenthesis that you used.
Brilliant. Love you for putting this up for us!!!!
Excellent teacher!
Amazing lessons! I learned so, so, much from this video. I will forever be gratefull.
Amazing Technology to provide this very detailed class.
I would suggest that you have explained that as far as radius (r) is our measurement unit, we will replace the degree (°) with (r) so one would easier understand why you removed the r from 2π when you placed it at 360 degree area at x axis (i.e 2 π is equivalent to 360° because 360° = 2πr). If you remove the degree from 360 it will be equivalent to removing the r from 2πr. In this way by analogy could people easier understand what you are talking about, as you jumped from measuring in degrees to measuring in radians with out enough explaining what you were doing .
@iqb62: this is about the UNIT circle. The radius, r = 1 (a unit, or one unit). Hence the 2πr or 2π(1) = 2π
I took Pre-Calculus in 11th grade and the course touched Trigonometry and Algrebra 2. This was back in 2006. To this day I still (sort of) remember the unit circle.
Easy to follow, great video! Much appreciated
I have never done trig in school, but this is very interesting to get a grasp on.
i'm here for the same reason, i'm an 8th grade student from Poland who finds school too easy and boring, especially math, because i'm really interested in it
At 8:00:40, the video leaves out the derivation of z^3. Here's how it can be derived:
z^3 = r^2(cos(2θ)+isin(2θ))(r(cosθ+isinθ)). Given i^2 = -1 and expanding, one gets
r^3((cos(2θ)cosθ-sin(2θ)sinθ) + i(sinθcos(2θ))+cosθsin(2θ))).
Applying the angle difference identity (4:42:54) and sum identity (4:45:41) explained earlier in this video, one gets:
r^3(cos(2θ+θ) + isin(θ+2θ)) = r^3(cos(3θ) + isin(3θ)).
Generalising to z^n can be proved using mathematical induction, for which one can find explanations by searching UA-cam or online elsewhere using 'De Moivre induction'.
Thank you!
I'm only in the 5 hour mark and why tf does derivation of r³ have that long of a direvation😭(isn't it just 3r²
@@ssureshk I used 'derivation' in the broader sense of 'a sequence of steps to get a result'. I did not mean 'derivative', which falls under calculus, a topic which this video does not cover. Hope that helps.
I remember doing advanced trigonometry in high school in my third year of high school had my 🧠 swollen 🤯 I appreciate my teachers for helping me ➗➖ 📚📖 🙏🙏🙏
7:57:25 De Moivre's theorem
Professor you are awesome 👏🏻
I'm just tired of not knowing trigonometry
I've decided that I'm going to spend 60 minutes each day on this
Day 1: √
My class just stuck literally all of this stuff on the end of my college algebra class and told me to learn it in two weeks.
Q (colon)
A (close parenthesis)
This is a good case for listening to a paid professional in a scholastic institution.
You know, I have been taught trigonometry and geometry in chunks that were never linked up or had stuff thrown in and we were told, oh you just need to accept that. But I have NEVER had this explained to me in a way that joins up the dots. I am a very visual and kinestetic type of learner and THIS IS PERFECT. I teach maths just to a basic level and this has given me such a greater understanding and all also given me ideas for my own lessons. Thank you.
Awesome, have a good day Chris Cain :)
Awesome video!
Wow I finally know what polar coordinates are. Went through uni not knowing
this is one of the best things on youtube! brilliant :)
360 degrees...makes a lot of sense, thank you
memorizing, common sense and language , all simple
Thank you so much ❤
Tons of thanks to professor 🙏🏻
Awaiting more of your lessons in other categories of mathematics
I have to thank you for this video, because the online course I'm taking is cretinous and doesn't have enough material so this helps! Thanks again! Cheers and Happy New Years!
yall complaining but my guy made it 9 hours bruh chill out with that
Thank you this couse is great for a beginner like me.
just started but had to say how grateful i am. I don't do well with memorization. My brain works with understanding not just memorizing and spitting it back out. finally, the unit circle makes sense. I was not getting the pi numbers and why they were there or how it worked, and as stated memorization was just not going to cut it. thank you so much! out of all the videos on UA-cam and class finally someone explained it!
6:41:44 isn't the factoring supposed to be (2sinθ - 3)(sinθ - 1) ? Cuz what he did will give a -3....... And so the Answer should be (0, π).
Yes bro, you are right👍
I'm stuck with trigonometric identities 🤯 do I need to memorize all of these? Especially the sum and difference 🤯
Fascinating mathematics, favorite branch of math I ever studied.❤
Thanks for sharing these matter
thank you... I am able to cope with my calculus class now
Just want you to know that your work is getting all over the world, I'm from Brasil and this helped me a lot!, thank you!
3:58:32 35 feet in the air means 33 ft on the ferris wheel.
Thank you. Excellent video. Grettings from Medellín