⭐️ 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
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)
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
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.
@@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...
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 ❌
@@waddlesthepig5350I didn't need the stuff after 4:30 3 years ago 😂. If it makes you happy just know that I can pretty much teach the whole course now😮 making it in some sense "completed"
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
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.
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
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!!!
its so fun going back and refresh the lessons from HS . . . . . . . . . . . . . not until u encounter new things in trig that your school havent teach u. this video deserves more
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
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? 😮
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)]
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.
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
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.
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
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!!!
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!
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 RUclips or online elsewhere using 'De Moivre induction'.
@@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.
22:00 - Arc length (s) derived formula in radians 25:24 - conversion of radians to degrees vice-versa Notes: θ - degrees AND radians if θ is constant so does m
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
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 RUclips to me I swear- I may be learning this really early, but I don’t care, it’s fun!
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.
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.
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!
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.
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 RUclips and class finally someone explained it!
4:43:05 There was absolutely NO explanation prior to this point about the relationship between values of cos and sin beyond "it's shifted forward by π/2", which doesn't explain how would subtracting angle from π/2 and removing the minus magically turns either function into its counterpart
4:06:32 If you use a period of pi/84, you can find the exact day that the temperature reaches 65 degrees. From there you subtract 24 hours to get a number less than or equal to 24 and that is the time at which it is 65 degrees. I realize that the question is specific to a day in a week rather than just the entire week.
I do not understand how did he find the horizontal shift. we literally don't know where the starting point is. why did he just shift right by 5 units(days i think).
@@Unkown242 He his actually basing the temperature off of a single day in a week rather than the entire week (as I thought). So 5 is 5 hours passed the start of the day (or period) which is 5am.
@@MisterMusicArchive from 12am midnight to 5am would be 5 hours. thanks. I went to a discord server and they helped me out there. its a public server called mathmatics.
2:48:14 this example implies that there is a continuous (and linear) motion of the Ferris wheel. If it were to have a mechanical failure or a random speedup in the middle, then the graph would be different.
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 .
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!
From around 7:28:00 to 7:37:31 there's no audio. If anyone needs it you can find it in the last 9 mins from the original video of that lecture: ruclips.net/video/fHfxw12BTOg/видео.html
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
I landed here on chance thanks to youtube. and looked at your channel. and I saw how you made videos about pretty much every topic in math. and more. As I am currently trying to learn computer science on my own, I have to tell you only one thing: SUBSCRIBED!!!
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.
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
Response to Brandon: Thanks a million for your response to my question about calculating the distance to a star using the known base of 186 million miles which is the diameter of the orbit of the earth around the sunm which takes six months to get to the opposite side. I'm rather dull when it comes to Trig (I never took trig before so it is all new to me) so I am slow. In your response you stated that the Tangent (angle of theta is 89.4 degrees) is the Opposite over the Adjacent. I'm not sure if I misled you but the base of the right triangle is 93,000,000 miles, not 186,000,000 miles. The 186,000,000 refers to the entire diameter of the earths circle around the sun. I did calculate 89.4 over 1 = O over 186,000,000 and cross multiplied both sides but got 16,628 not 1.776 ( I'm not counting zeros right now). Is there something I missed or got wrong ? I agree Trig is amazing. Yesterday I called my local high school math, geometry trig department but they were totally unhelpful. If I can figure this out, I will be able to map distances to stars I can see with my naked eye but it takes six months to take the second measurement. The paralax is very very small as you can imagine.
Factoring at 6:39:08 is not right. It should be: (sinƟ - 1)(2sinƟ - 3) = 0. So sinƟ = 1 and sinƟ = 3/2. Anyhow this is great trig series! Thank you to the author!
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.
@@strawb3rrypink817 i remember last year half my class failed trigonometry and i got a rly good grade. Only tip is to memorize the cos sin and tan of angles like (π/2) or (π/2+x) etc and you'll probably ace it
@@strawb3rrypink817 no worries haha but u also have to know how to convert by adding or subtracting 2π to angles so u get the coterminal one I thought that's something you probably knew but just making sure you rly ace it
1:28 part of a doc I once saw showed how a certain people used base 12 for this reason. Easiest way to make combinations and get any whole number eg: splitting/selling grain etc.
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 ➗➖ 📚📖 🙏🙏🙏
Thanks for sharing!! Is it possible to add the option of having captions in the video? I am not saying that you have to add them, but with that option enabled other people or even me can add them in the future...
Thank you so much I am in 7th grade and it helped me so much understand these concepts better. Thank you so much! Where can I find more homework problems?
A little remarking: At 14:40 you wrote a wrong equation: You wrote 4π/6 = π/3 But that isn't true! The right version is: 4π/6 = 2π/3 Otherwise thanks for the video!
⭐️ 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 😮 🙀
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
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?
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.
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 RUclips
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=?
come back and complete it lol
@@waddlesthepig5350I didn't need the stuff after 4:30 3 years ago 😂. If it makes you happy just know that I can pretty much teach the whole course now😮 making it in some sense "completed"
dont give up ! we are rooting for you!
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
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 :))
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.
@@averyinterestingpineapple6038 Bro was from future 1.9 M
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
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
The Best teaching I have seen on this subject very well done, cheers.
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
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 😳
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👁👍🏾
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
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)
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.
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
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.
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.
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
My math class doesn’t go this deep into trigonometry. Thank you
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!!!
THis has helped me understand more clearly and I'm able to follow my instructor during his lectures. Thank you :)
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!
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 RUclips 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.
One of the best online courses! Thank you for the thorough, fine work!
22:00 - Arc length (s) derived formula in radians
25:24 - conversion of radians to degrees vice-versa
Notes:
θ - degrees AND radians
if θ is constant so does m
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
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 RUclips 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.
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😂😂
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.
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
Thanks man. I am an undergraduate student but still didnt understand high school trignometry until i saw this video. You are a great teacher
Man, this helped me a lot. I am forever grateful, I hope one day I can become a great teacher as you are.
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!
1:10 To draw better circles, make the required motion with your shoulder and keep your hand rigid.
I had 4 years of Design school and not one professor ever told me that. I will definitely be practicing this!
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.
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 RUclips and class finally someone explained it!
Fantastic. Very clear and easy to understand. Thank you.
4:43:05 There was absolutely NO explanation prior to this point about the relationship between values of cos and sin beyond "it's shifted forward by π/2", which doesn't explain how would subtracting angle from π/2 and removing the minus magically turns either function into its counterpart
legend not gonna lie.keep up the goooooooodo work
4:06:32 If you use a period of pi/84, you can find the exact day that the temperature reaches 65 degrees. From there you subtract 24 hours to get a number less than or equal to 24 and that is the time at which it is 65 degrees.
I realize that the question is specific to a day in a week rather than just the entire week.
I do not understand how did he find the horizontal shift. we literally don't know where the starting point is. why did he just shift right by 5 units(days i think).
@@Unkown242 He his actually basing the temperature off of a single day in a week rather than the entire week (as I thought). So 5 is 5 hours passed the start of the day (or period) which is 5am.
@@MisterMusicArchive from 12am midnight to 5am would be 5 hours. thanks. I went to a discord server and they helped me out there. its a public server called mathmatics.
@@Unkown242 I know about it.
2:48:14 this example implies that there is a continuous (and linear) motion of the Ferris wheel. If it were to have a mechanical failure or a random speedup in the middle, then the graph would be different.
@zmfd Thanks
15:23 there is an easy method to convert angle into radians
We have to multiply that angle into 180/π
Finish the entire course 💪💪 It's time for doing some exercise
Best video ever I have seen on trigonometry
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
Amazing lessons! I learned so, so, much from this video. I will forever be gratefull.
Thank you for sharing this lesson, it is decent and useful.
This videos length proofs that it's made with pure dedication
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!
From around 7:28:00 to 7:37:31 there's no audio. If anyone needs it you can find it in the last 9 mins from the original video of that lecture: ruclips.net/video/fHfxw12BTOg/видео.html
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
this is one of the best things on youtube! brilliant :)
How appreciatable that many of the teachers were not able to teach us as good as he did
I landed here on chance thanks to youtube. and looked at your channel. and I saw how you made videos about pretty much every topic in math. and more. As I am currently trying to learn computer science on my own, I have to tell you only one thing:
SUBSCRIBED!!!
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 :)
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
Brilliant. Love you for putting this up for us!!!!
found the perfect channel of the year, heart math
Professor you are awesome 👏🏻
Explained the trigonometry in a very very simplified and clarified manner. God bless you and your family please.
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!
Thank you to you and all these special people who took the time to share their knowledge gracefully, asking nothing in return!
Response to Brandon: Thanks a million for your response to my question about calculating the distance to a star using the known base of 186 million miles which is the diameter of the orbit of the earth around the sunm which takes six months to get to the opposite side. I'm rather dull when it comes to Trig (I never took trig before so it is all new to me) so I am slow.
In your response you stated that the Tangent (angle of theta is 89.4 degrees) is the Opposite over the Adjacent. I'm not sure if I misled you but the base of the right triangle is 93,000,000 miles, not 186,000,000 miles. The 186,000,000 refers to the entire diameter of the earths circle around the sun.
I did calculate 89.4 over 1 = O over 186,000,000 and cross multiplied both sides but got 16,628 not 1.776 ( I'm not counting zeros right now). Is there something I missed or got wrong ?
I agree Trig is amazing. Yesterday I called my local high school math, geometry trig department but they were totally unhelpful. If I can figure this out, I will be able to map distances to stars I can see with my naked eye but it takes six months to take the second measurement. The paralax is very very small as you can imagine.
Really I was so curious to learn trigonometry but I was looking up for a perfect teacher and that was u
The Audio isnt available from 7:28:00 to 7:36:42. Please look into it.
Factoring at 6:39:08 is not right. It should be: (sinƟ - 1)(2sinƟ - 3) = 0. So sinƟ = 1 and sinƟ = 3/2. Anyhow this is great trig series! Thank you to the author!
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 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.
I just started learning trigonometry in the beginning of this month, I like trigonometry a lot
I hate it I’m so bad so I’m trying to speed run trig by watching this 🏃♀️
@@strawb3rrypink817 i remember last year half my class failed trigonometry and i got a rly good grade. Only tip is to memorize the cos sin and tan of angles like (π/2) or (π/2+x) etc and you'll probably ace it
@@Jo_Es_Chess_Channel o,o thank you so much genuinely lmao
@@strawb3rrypink817 no worries haha but u also have to know how to convert by adding or subtracting 2π to angles so u get the coterminal one I thought that's something you probably knew but just making sure you rly ace it
1:28 part of a doc I once saw showed how a certain people used base 12 for this reason. Easiest way to make combinations and get any whole number eg: splitting/selling grain etc.
Amazing Technology to provide this very detailed class.
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 ➗➖ 📚📖 🙏🙏🙏
Thanks for sharing!!
Is it possible to add the option of having captions in the video? I am not saying that you have to add them, but with that option enabled other people or even me can add them in the future...
Great thanks
Very good video! I have 3 more years of home schooling my son. The final 2 years will be spent on your trigonometry course and calculus course!
Great course. Thank you so much for this.
Good, superb 👌 👏 👍 🙌 😀 😎 👌 👏 👍 🙌 😀 😎 👌
360 degrees...makes a lot of sense, thank you
Thank you would be very little to show how grateful I am .
Just loved your efforts ; would like to have more of these ❤❤❤❤❤
Thank you so much I am in 7th grade and it helped me so much understand these concepts better. Thank you so much! Where can I find more homework problems?
In trig identities and negative angles (4:15:xx) it is better to introduce sin(-x)=-sin(x) and cos(-x)=cos(x) before go into tan(-x) etc.
Hi can u make plz plz a full course on organic chemistry!!! I love this content and it'll gonna be really helpful
Fascinating mathematics, favorite branch of math I ever studied.❤
1:02:07 something easy to remember.
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
A little remarking:
At 14:40 you wrote a wrong equation:
You wrote 4π/6 = π/3
But that isn't true!
The right version is: 4π/6 = 2π/3
Otherwise thanks for the video!
oh yeahh ! thanks for pointing it out
I know this is random but I just love how his handwriting is better than me drawing a crappy triangle
Thanking you forever wouldn't be enough🦾
bro this channel needs more attention
its really great for the learners
Tons of thanks to professor 🙏🏻
Awaiting more of your lessons in other categories of mathematics
memorizing, common sense and language , all simple
7:57:25 De Moivre's theorem