“So I’m going to construct a unit circle here. So, construct a unit circle. So this right here is a unit circle, circle of radius one. So construct a... unit circle. That’s a unit circle.” Nice
@Personal-jr9rn3 жыл бұрын
Yeah that is the only thing that bothers me from learning from him but still I can't find any one better than him
@joranmulderij3 жыл бұрын
Most Khan Academy videos are pretty slow paced. I only tend to use them when I really get stuck on something. But in case I do really get stuck, Khan Academy almost always makes me understand it.
@manindrademel57793 жыл бұрын
I learnt more in the first two minutes of this video compared to the 1 hour and 40 minute class i had today
@TheCoon17893 жыл бұрын
True
@neutrogemax8494 Жыл бұрын
@brayanmani7112well yeah how long are your classes
@theromanempire35602 ай бұрын
@brayanmani7112 in university they will be 2 hours long
@Alberpinypon8 жыл бұрын
This video is terrific. We all think that the basis are always clear, but without realising we end up doing calculations without thinking what everything means. Just a great way of explaining sir. Hands down.
@frostbitepokin95205 жыл бұрын
Alberto counterCOCKwise
@jakobsime41902 жыл бұрын
@@frostbitepokin9520 ?
@DualWielded_ Жыл бұрын
cap
@LittlePrincessatB-6123 жыл бұрын
This video has saved me from my teacher's slides. Thank you!
@xgg40173 жыл бұрын
i feel like in class its just taught to you as something just is the way it is, i rly appreciate these videos online that actually demonstrate the background explanation for why things are the way they are....like if something makes sense because of where it is derived from, then its like so much easier to remember thanks for the amazing vid :)
@n0lain7 жыл бұрын
Countercockwise Joke's on me I'm about to fail this subject test
@nickbeats98834 жыл бұрын
Did you fail?
@n0lain4 жыл бұрын
@@nickbeats9883 Nah pretty sure I got like an A or a B. Ended the class with like an A- so that's a dub
@Theweirdo23-w4e4 жыл бұрын
@@n0lain that was 3years ago I don't think I'd have remembered at all
@n0lain4 жыл бұрын
@@Theweirdo23-w4e to be fair I 100% forgot about my comment, I came back cause of the notification
@g.3rd7 ай бұрын
@@n0lain Did you forget about this one too 3 years later?
@authenticwarrior78779 жыл бұрын
superb teaching skills....
@frostbitepokin95205 жыл бұрын
authentic warrior counterCOCKwise
@criticalangle902 жыл бұрын
This actually gives context to complex numbers. It actually makes sense to someone like me who hates imaginary numbers. THANK YOU!!!!!!!!
@MrArthur23123 жыл бұрын
7:40 the angle is actually from x axis right side to the complex argument clockwise thts why its pi+the angle
@emilycaballero60527 жыл бұрын
"These are not the thetas you are looking for."
@renatoh.santos52125 жыл бұрын
I know hahahahahah
@Jo_Es_Chess_Channel5 жыл бұрын
Respect. Only sexual joke that doesn't involve countercockwise
@ridanoorani35255 жыл бұрын
How do we go back to the (a+bi) form?
@Superegio4210 жыл бұрын
I stay up late to watch stuff like this.
@EXHellfire6 жыл бұрын
so badass
@frostbitepokin95205 жыл бұрын
counterCOCKwise
@ginaxs79752 жыл бұрын
2:30am😭
@jordanbonner84053 жыл бұрын
This finally lit the light bulb. Thank you
@westeast62298 ай бұрын
Im an Algerian student who is in his last year of high school and unfortunately this is in our program, you are actually a god send my friend
@stardust-reverie4 жыл бұрын
countercockwise
@azizahputri632 Жыл бұрын
Wow the explanation is very clear, thank you so much sir, you really helped me!
@AShad9510 жыл бұрын
Hahaha "counter cockwise" at 11:50. Great video though, very helpful
@theartemys7 жыл бұрын
Yeahh XD
@Personal-jr9rn3 жыл бұрын
omg i don't understand where is the issue
@RedBar3D10 жыл бұрын
The part at 3:50 wasn't all that obvious to me. What made me "accept" the statement was thinking of the two triangles formed; they're uniform. And since the hypotenuse of the smaller one is 1, the x- and y-coordinates must be r*cos(theta) and r*sin(theta) respectively. The books I've had and have tend to show that this holds for right angle triangles (they don't even mention the unit circle) in the first quadrant, and then state that it holds for all quadrants (ie. not actually proving it). I'm not sure whether it's me or the books, I refuse to accept things without solid proof. Thank you for the video :)
@Ескендір-б5р Жыл бұрын
Its because of similar triangles If triangles have equal angles they are similar and that means that ratio of sides are equal
@sdeshpande0910 жыл бұрын
The explanation for deriving theta can be much simplified if r was calculated first,and then use the definition of tan theta to derive theta.
@mohanadabdulrahim72024 жыл бұрын
2020 and still learning from him
@chngkai27443 жыл бұрын
it is 2021 now
@fikrattalibli24336 жыл бұрын
The whole complex numbers in 12 minutes!
@pnkmimi1323 Жыл бұрын
thank u for actually explaining it properly
@InSterquiliniisInvenitur5 ай бұрын
The reason for using r cis (θ) was not explained by my textbook in a way that made sense to me. This video helped a lot.
@WSTSWISS4 жыл бұрын
this was soo good! thanks
@GtaRockt9 жыл бұрын
thank you so much. I never understood why the angle has so many different ways to calculate, considering if a or b are either positiv or negative. you are the man!
@frostbitepokin95205 жыл бұрын
Lobster with Mustard and Rice counterCOCKwise
@Permafrostrock10 жыл бұрын
Straight and clear explanation. I would have loved it before we first used the polar form in geophysics :D
@dalenassar91522 жыл бұрын
THANKD MUCH FOR ALL OF THE LESSONS!!
@Raphael-ql9pf3 жыл бұрын
7:50 my own learning checkpoint
@machinegunnasty11244 жыл бұрын
Does he have a video on Polar to Cartesian?
@code58293 жыл бұрын
Working from the problem is key
@martinuusss8 жыл бұрын
I learnt polar coördinates in the form of (r, Phi) (Phi = your Theta, guess that's not universal) which IMO makes it even clearer, you go 'r' away from (0,0) with an angle of Phi. Example: (r, phi) = (2, Pi) -> Z = -2 (+ 0i). (r, phi) = (sqrt 2, 1/4 Pi) -> Z = 1 + 1i . Thanks for your video, and I must admit, 720p + a new mic makes for a much better experience than your older complex number video's from 2008 ;-)
@sarimansari97013 жыл бұрын
Well.. In terms of understanding... I lost it from 2:06.... But I can surely say that whatever happened after that IS really interesting... ✌
@garrettremaley67379 жыл бұрын
OMG thank you so much! You've quickly explained what my teacher couldn't explain in weeks.
@frostbitepokin95205 жыл бұрын
Garrett Remaley counterCOCKwise
@markbossman510310 жыл бұрын
SAL YOUR STILL THE MAN!
@I-VisiBomb-I9 жыл бұрын
+Mark BossMan You're.
@markbossman51039 жыл бұрын
give me a break loser
@I-VisiBomb-I9 жыл бұрын
+Mark BossMan says the guy that learns calculus but doesn't know simple grammar.
@jacobm82428 жыл бұрын
+I VisiBomb I This is a math lesson lol, not english.
@I-VisiBomb-I8 жыл бұрын
Jacob Mikeska in which you use letters from the English language.
@klc0322879 жыл бұрын
Like the new mic.
@billtruttschel10 жыл бұрын
Some trig books would abbreviate the last part as sqrt(13)CIS(2.55).
@PimpMatt07 жыл бұрын
Liberal arts have taken over the term CIS for Cisgender.
@code58293 жыл бұрын
They added new function “trans” to coexist with CIS
@govindnair31357 жыл бұрын
Sir , you could have used triangle of vector addition,and resolution of r into 2 components.
@JustTruth-x7g21 күн бұрын
You're amazing !
@neyazahmad362 Жыл бұрын
Amazing 😊😊
@samuelkoomson53693 жыл бұрын
Very helpful.
@AlessandroZir2 жыл бұрын
thank you! very useful and clear;
@emilycaballero60527 жыл бұрын
Thank you for saving my life
@erd447 ай бұрын
Thank you, it was very helpful. For me, finding theta would have registered better in degrees, idk if anyone else feels that way.
@redwestanimation541 Жыл бұрын
since pi is 180 you're supposed to subtract not add
@milesemanuelpaavola79946 жыл бұрын
Thank you again, your videos can be a Godsend at times. :-)
@michaelhawkins80955 жыл бұрын
Hey, anyone.....at 3:41, Khan said that x is sin and y is cos. I thought that it was the other way around.
@yashesvi-raina4 жыл бұрын
Thank you!
@Darkreign14 жыл бұрын
is it okay to do this in degrees or does it need to be done in radians?
@milliebean998 жыл бұрын
Question: how would you find the modulus argument form of JUST a real number or JUST an imaginary number (ie: -20 or 3i)? My textbook has questions like these but I have no idea how to go about solving it?? I thought I was good at maths lmao
@Klikmac8 жыл бұрын
well the argument of just a real number would be zero and the argument of just a complex number would be 1/2pi as they're just sitting on their axis
@furqaanilahi8078 Жыл бұрын
@@Klikmac my question is since the real number is negative, then it is on the -ve part of real axis, is the angle pi??
@jibby12744 жыл бұрын
how did you know to add pi to theta
@Optimistic300215 жыл бұрын
I was lost at -0.59 + pi. Why wasn't the calculator correct? Something about needing to shift by adding pi, but that was confusing to me.
@michaelhawkins80955 жыл бұрын
And...stop laughing at his 11:50....very mature KZbin...very mature.
@budahbugahbugah65737 жыл бұрын
Lol im so immature as soon as I heard counter cockwise I rushed to the comment section to make sure I wasn't just hearing things.
@durgaipriyads72058 жыл бұрын
GGGGGGreat explanation sir
@Mastermism5 жыл бұрын
This has been very helpful, thanks.
@josephrichardson556110 жыл бұрын
Is this the same when working out British numbers?
@suryavikramrizal34629 жыл бұрын
thanks Sal...
@richardlighten70767 жыл бұрын
excellent video , hugely helpful **
@ginaxs79752 жыл бұрын
Where does the e come into this? Like re^(i theta)?
@luisangelzeferinocuautle33063 жыл бұрын
What program do you use?
@hamburgeor65677 жыл бұрын
I love you Sal Khan
@kaethis Жыл бұрын
11:50
@mch867 жыл бұрын
thanks but I GOT ISSUES ON TRIGONOMETRICS AS WELL I WILL SURELY WATCH IT AGAIN AFTER A TRIG REVIEW
@stefanovetri60583 жыл бұрын
Couldn't we use inverse sin or cosine to find theta??
@seeuclon7 жыл бұрын
can we now figure out what r and theta R?
@comprehensiveboycomprehens87867 жыл бұрын
Pause at 3.20. Think.
@arundathivarma72098 жыл бұрын
this was very helpful...thank you :)
@nikonoy35644 жыл бұрын
How did you get cos(theta) is it same as cos(pi - theta)
@mohammedhafizurrahman37617 жыл бұрын
314k views and only 580 likes??
@siddharths24436 жыл бұрын
Cuz mostly people use the site,hence they view the embedded version of the video where they cannot like the video.
@frostbitepokin95205 жыл бұрын
counterCOCKwise
@tahseenalaa703010 жыл бұрын
thanks so much :)
@abloodorange52333 жыл бұрын
Why my teacher just doesn’t explain exactly what the question will ask like you did only God knows. Wasted a week of my life.
@muhammadnafees75148 жыл бұрын
sir which application on computer for lecture like as a white board?
@compleks19978 жыл бұрын
Honestly it looks like it's MS Paint
@boshboshish8 жыл бұрын
I don't know why did you put the angel in rad should it be tan -1(-2/3) = -33.6 degree right away ?!!
@ghassan3088 жыл бұрын
No, Precalculus is part of Calculus and in calculus you use radians for the trig functions
@frostbitepokin95205 жыл бұрын
He did it because it’s counterCOCKwise
@evanbyrne31929 жыл бұрын
how come its cos teta is that not the tan quadrant?
@yousefhamdan31885 жыл бұрын
It's 3 AM . Why I'm watching this
@frostbitepokin95205 жыл бұрын
Yousef Hamdan because counterCOCKwise
@AleLox Жыл бұрын
Miguel Diaz
@oneinabillion6546 жыл бұрын
Hi, is a complex number always relative to the origin
@furqaanilahi8078 Жыл бұрын
I think yes, sorry a little late (4 yrs late 😂)
@oneinabillion654 Жыл бұрын
@@furqaanilahi8078 is ok, it wasn't the right question 😉
@Tensho_C4 жыл бұрын
This comment section is immature af I love it
@scarleteyes4156 жыл бұрын
Why did 90% of people in the comment section not understand? I don’t get it, what is it that you don’t understand? I may help.
@sasakoncar5 жыл бұрын
i(t) = 20·cos(18570·t − 2.8798) how to get rectangular of this?
@sphinx193 жыл бұрын
tan-1(-2/3)=-33.69 degree??/??
@Assault177 ай бұрын
Change ur calculator to radians 😂
@vnsomeshwar6 жыл бұрын
isn't this pretty much the same thing as vectors?
@allenburt14756 жыл бұрын
Just wait till roses and crap
@Tyler-kh6gp3 жыл бұрын
Ngl, I upvote all Khan Academy videos before watching them because I already know they're going to be good
@mrmathmonkey95825 жыл бұрын
quick question can you do this questions in degrees without using any radians...?
@TheCherryify10 жыл бұрын
Why can't you just get theta right away by doing theta = arctan2/3 then pie -arctan2/3 = 2.55?
@n.t30267 жыл бұрын
woah
@josephrichardson556110 жыл бұрын
I don't get it try and do this question why is every e.g. Got - as the real number and not plus instead. Try z equals to 5 plus 2j.
@normal_person12 жыл бұрын
I DIDN'T GET IT
@Drderp-hd5bb6 жыл бұрын
wish u kept it in degrees
@JustANobody9104 жыл бұрын
This video didn't really help me much....I need more example problems
@susannamenlamenla82837 жыл бұрын
"
@Hazit9010 жыл бұрын
I love you Sal. (no homo)
@LMFAO918 жыл бұрын
complete waste of time, should have just shown the last 5 minutes
@MattMelon5194 жыл бұрын
I have no idea what the hell you are talking about.