Parametric equations 1 | Parametric equations and polar coordinates | Precalculus | Khan Academy

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Introduction to parametric equations
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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Опубликовано:

7 сен 2024

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Комментарии : 221

@ScrawnyCFB 4 года назад

I have my Calc 2 final tomorrow morning at 7 am and I would absolutely love to be in that car driving off of the cliff

@ScrawnyCFB 4 года назад

@@Ryan50Ryan I ended up getting a 95%, which was a MASSIVE surprise

@aadhityakumaran2016 3 года назад

Well That's a world with no air, you would have died without driving off

@lelo8244 3 года назад

@@ScrawnyCFB congratulations ❤️❤️❤️❤️❤️

@SortaFresh 3 года назад

@@ScrawnyCFB yayy nice job

@hozayrodriguez8968 Год назад

❤❤❤❤❤😂😂😂😂

@codyhufstetler643 11 лет назад

as a mechanical engineering student, relating this to physics helped immensely. thank you.

@Wasoska 5 лет назад

Same

@bychen5011 3 года назад

It's been 8 years. How has ur life changed?

@assemsarimova4969 2 года назад

@@bychen5011 i wanna know too

@godvegito3686 Год назад

How has your life changed?

@probably_meg 12 лет назад

This man has literally saved my life in high school. And will still be there in college...haha I wish every teacher of mine taught like him, learning is SO EASY.

@real_john_doe 6 лет назад

Why am I being taught this at the very end of Calc 2?

@Lucky10279 5 лет назад

Same here. I'm confused as to why this video is categorized as precalc.

@Wasoska 5 лет назад

Same

@rayyfire5738 5 лет назад

@@Lucky10279 this topic is involved in precalculus textbooks

@Lucky10279 5 лет назад

@@rayyfire5738 Clearly, it varies by curriculum, as a lot of other people said they're learning it a lot later.

@rayyfire5738 5 лет назад

@@Lucky10279 the curriculum is not the textbook, of course it would vary by curriculum

@Direwolf56 11 лет назад

"And this car is not just sitting on the cliff, its driving off of it." I love Sal that much more now.

@drutledge884 8 лет назад

Why is this video more helpful than my pre-cal teacher?

@Gelenvader3 7 лет назад

when i saw projectile motions i got so triggered :( ptsd got me

@Bush21122 10 лет назад

I love this dude .. lol thanks Sal

@AliceWeeksAli 6 лет назад

as a Brit this guys voice and positive attitude is a welcome break honestly lmao

@Ccccccccccsssssssssss 5 лет назад

Thanks, this was really helpful in understanding WHY we're learning parametrics!

@theadel8591 5 лет назад

Your comment is new

@mysticmonk3456 3 года назад

Ah yes, the very practical "driving off a cliff problem" ; my favorite.

@ringo38825 14 лет назад

brilliant! I'm a math major and a Trig tutor and this lecture has given me a new method of teaching parameters.

@cedricfrancis5662 3 года назад

This is a very good video on the concept of parametric equations. I've known about them for some time now but couldn't link them to everyday life until I came across this video. Now I won't forget about parametric equations, because i now grasped the concept fully, thanks to this video.

@AliveDog 12 лет назад

me too man. 3 weeks till final and I'm stuck on this shit.

@physicsboi1744 3 года назад

lol its been 9 years, do you still use maths often in ur career? Thx just asking :)

@Jonnemanne 14 лет назад

I really like these clearer high-def videos ! It'd be great if you could redo the projectile motion videos in HD. In my opinion there's nothing better for the beginning/struggling physics student than clear, easy-to-follow AND read fundamental videos. :) thanks Sal, you've done an awesome job ! Greetings from Finland !

@carlosr6547 5 лет назад

Finally!!, somebody that can explain it so simply, thank you so much

@Reydriel 8 лет назад

So that parameter 't' is like a third variable or a third axis? If you used a three-dimensional graph it would be the same thing, right? (if you look at it from the plane of the x and y dimensions only, of course)

@EsaldaH 13 лет назад

@ForeverWiked acceleration : ax=0, ay= -g (gravitational acceleration on earth) You integrate the acceleration to get the velocity -> velocity : vx= 5, vy = -gt (don't forget the initial conditions, here the velocity at t=0) Then you inegrate the whole thing again to get the position -> position : x=5t+10, y= -gt²/2 + 50 with g~10m/s² Again, initial conditions. Position at t=0.

@binayakchowdhury405 10 лет назад

Nicely explained. Thanks to You tube and Khan Academy.

@theodoresweger4948 3 года назад

I loved putting this in my HP prime using the parametric app, thanks and I have just been studying kinematics beautiful thank you.

@nas-cf1wy 10 месяцев назад

If you want to know when the car exactly hit the ground. Solve for t using y=0 and find value of t

@bensculfor9706 10 лет назад

Such a good video. We have been learning about this stuff in further maths but we were never told about when this stuff could be used.

@niconikko 12 лет назад

For God so loved the world, he gave us Mr. Khan. Sal is the next savior!! Thumbs up if you agree.

@HockeyMan-kd7yj 6 лет назад

Exactly what I needed thanks!

@Travoid 11 лет назад

Pa-RAMETER. Parameter. ...pa-rameter.

@Macdawg347 13 лет назад

I love your teaching style, very good job!

@punaydang2948 5 лет назад

can someone explain at 4:24 from where t^2÷2 came?

@topdown4705 4 года назад

I believe it's in his projectile motion videos www.khanacademy.org/science/physics/one-dimensional-motion/old-projectile-motion/v/projectile-motion-part-1

@shamikpatro 4 года назад

Generally speaking, if you integrate acceleration twice with respect to time, you should get an equation with (t^2)/2 as one of the terms. Here's a helpful crash course video on Integrals (kinematic equations) if you're interested in finding out why: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-jLJLXka2wEM.html

@stealth834 15 лет назад

I am a math tutor and your videos provide me with another method to get information across to students. Thanks for the great work!

@ssj4edits840 3 года назад

Legends say you're still giving informations to students...

@ClickGoesTheMouse 12 лет назад

Why does he use t^2/2 (4:25) ?

@ubong-abasiakpan1771 11 месяцев назад

Y is acceleration due to gravity negative (-10m/s²) Based on equations of motion, for any body moving downwards (g) is positive, and if it's projected upwards it's magnitude becomes negative cause it's acting in an opposite direction to (g) So sir explain why 10m/s² is negative Cause am confused at that point 😕

@Raiyun166 15 лет назад

I learnt it during precalc. But naturally it applies in calculus too.

@TuscaniManiac 15 лет назад

may god bless you man..just keep doing those videos ..they're super helpful !! 5 stars !

@klotweev 14 лет назад

@restituted Because, he set the equation equal to zero(the y axis being the height(when would the car be at zero height, or hit the ground)), and the equation was then 0 = 50 - 5t^2. So, he had to figure out what t would have to be for 50 - 5t^2 to equal 0. If t = the square root of 10, then the square root of 10 squared = 10. 50-5(10) = 0. So at the square root of 10 seconds, the car hits the ground.

@davenhunt 15 лет назад

The mass would be used in calculating the force on the car (or the ground), or some other information. If the car had no mass, gravity would not affect its motion. In a vacuum, all masses would behave in exactly the same way, so the equation covers objects of any mass.

@Lyxtwa 9 лет назад

I didn't know that there was a specific name for this. This would have been kind of useful to know before working with Rates of Change differentials.

@MountainNZ 11 лет назад

Oh God. Thank you. Finally I see why. Why is this not the first thing we get taught?

@zack_120 2 года назад

8:24 - Sal's visual scaling accuracy needs to improve in order to make this channel even better :)

@toasty4000000 11 лет назад

parameter. parameter. parammmmeterrrr. hahaha

@00JosefK 14 лет назад

The car off the cliff problem always makes me think of Toonces the driving cat.

@JordanMedina 13 лет назад

thanks man this cleared things up!

@rommelram1lovr2 13 лет назад

Hey!...Sal...More power!...(is it ok to say then that the Projectile Motion videos are mathematical analyses of one-dimensional variables (h or delta D)...the 2-Dimensional Projectile Motion...of two-dimensional variables (delta D & Ave. Velocity)...the Prametric Equation...of three-dimensional variables (x, y, & t) or are they...Alll...3D analyses???)...tnx! :D

@saharaicaldera331 11 лет назад

"We're on a planet that has no air.. we're in a vacuum" LOL why was that funny to me

@ollera18 11 лет назад

can someone please link the video that explain the t^2/2 for the y(t) equation??

@monahusseini6876 6 лет назад

usually the equation of the curve of an accelerating object is x=1/2a.t^2+Vi.t+Xi , where you can substitute x with any dimension and i is the initial point. This is a physics equation related to a(acceleration), v(velocity) and position(x,y,z,...)

@findo9615 5 лет назад

@@monahusseini6876 u think he waited 5 years for an answer lol

@jacoman1234567 15 лет назад

Does the mass of the car have any influence on the downward motion? Or is it taken in by the projectile curve formula?

@purplefire5 10 лет назад

all right so i have some questions and any help is appreciated! *I'm just learning this and so far I've really only seen the conventional f(x)= x + a (or trig/rational functions etc.) basically where y or f(x) is on one side and the equation is on the other and that suffices to describe the function. But I've never seen two equations describe a single function and i want to know why this is suddenly happening (i get that the two equations show where the object with respect to time) it's just a function has never been described with two equations for me and i feel like I'm missing something here why is this extra description needed (I know it's a weird question) *Also what is a parameter exactly, is it the same thing as a variable, like for an equation F(x)=cos2x is x the parameter????? *Finally, under what conditions/or what type of function do we need something like this where we need a pair of equations to describe the function? I haven't gotten my textbook yet and all I have to go off of are my notes so i would really appreciate the help THANKS AGAIN!

@shibbyness 14 лет назад

THIS IS REALLY GOOD!

@stramelhouse 14 лет назад

woah. Thank you so much.

@jacoman1234567 15 лет назад

Thanks for clearing out my mistake :)

@RSA_Shock Год назад

Hey this was made on my birthday

@microhaxo 14 лет назад

@restituted 0 = 50 - 5t^2 Solve for t.

@paperorpaper 15 лет назад

Sal can you please make a basic gemonetry video? I was going to start practicing but I have no idea what to do.

@agjehj 13 лет назад

wow.. you seem to be enjoying this. a lot. and pretty colors :)

@Naruto0519 13 лет назад

@HoorayforOranges True true! It's not confusing like teachers always make it seem!

@veralau93 14 лет назад

thanks that was fantastic!

@winstonlee3687 3 года назад

ratio

@nomthethomaseko1833 Год назад

thank you

@qualquan 2 года назад

Parametric = multi DGN per IGN? For example polar coords

@bboydjoe 14 лет назад

@mechwarreir2 its in calc too, (calc bc to be exact)

@CJEF1996 12 лет назад

this is the wrath of khan

@COYADD 11 лет назад

How come on my graphing calculator the length of the line ends depending on t? Ex: x(t)=2t The line will only go 2 to the +x direction. But what if t=2? Then x would be 4, but my calculator will only go a certain specified distance.

@tpstrat14 4 года назад

Well I think I may ditch my textbook. He’s such a great teacher !

@Danielxyoon 12 лет назад

i was wondering..do you use the mouse to draw these things or is it like a smart board?

@lousyindian 11 лет назад

3:20 Purrramitterrr

@arandompersononyoutube3739 4 года назад

2:06 Assuming that we are in a planet and there is no air and no forces like friction etc ,we are in vaccum 4:15 how gravity comes? Please could you please explain the topic , I can't understand clearly.

@adamsowinski9297 3 года назад

did you resolve it, i dont get it too

@Joesire 12 лет назад

yes

@rolfch1p 15 лет назад

nice videos!

@LoneAssassinX 15 лет назад

Great!!

@RachelSadoff 12 лет назад

THANKYOUTHANKYOUTHANKYOU

@williamjohnson9248 12 лет назад

im 11 and i can understand this and my friend is a ginesous (and i misspelled that sorry for my compertance ) and he diden't understAND IT ;)

@dbmasters 13 лет назад

@Lamboragon if you don't like the video, find another one that takes your fancy out of the 396 other videos on parametric equations.

@dadinggo 4 года назад

Thank God Khan doesn't use imperial like my Calc book. I'll never understand smh

@CuteAnimeJunkie 14 лет назад

Thanks so much! This really helped me n_n

@mamishmash 12 лет назад

try the whole of vector calculus in 4 days!

@anandar773 4 года назад

superrr...

@Tucktasticationister 13 лет назад

I made my RU-vid account to listen to free music.... I never thought I would subscribe to a math teacher! haha

@r0b0bert 14 лет назад

Khaaaaaaaan!

@NexFuturex 11 лет назад

I really wonder thathow to know salman khan all of things . really thanks.

@fatimadarling9656 5 лет назад

How is this precalc when it's part of my last sections in Calculus 2?

@benjamincheung4999 2 года назад

why are you using t^2/2?

@1Rab 12 лет назад

how on earth do you draw such perfect lines~!

@Atson3003 6 лет назад

Rab the software locks the cursor in a straight line ....

@TheMissclassyg 12 лет назад

wow...

@thelsdj 15 лет назад

No, mass has nothing to do with acceleration of gravity. A ping pong ball and a golf ball would have the same path if there was no air resistance.

@Naruto0519 13 лет назад

He must have gone to college like 20x with different majors each time to be this damn smart D: That's a lot of money T_T

@mitchwulfman 12 лет назад

haha, khan always has my back.

@alihajjar8 7 лет назад

"This is WHY" period

@akbvr 12 лет назад

Mr thompsons class ftw!

@purplefire5 11 лет назад

lol i have the same problem my teacher goes WAY TOO FAST but honestly the best tutorial for calculus is patrickJMT (his username on youtube) so you just type in the topic or chapter you're in and his name at the end and search, if he has a video on it his name comes up HONESTLY he has absolutely every topic explained with RLLY good examples that he clearly explains, he is the only reason i have an 87 in calc. just try looking him up he rlly helped me

@loverofbeats 14 лет назад

amazing! :D

@braineedly7543 2 года назад

at 4:21 why over 2? Where did it come from?

@benjamincordes207 9 лет назад

Thank you so much. Now i finally get it.

@HockeyMan-kd7yj 6 лет назад

How do you write so well with a cursor?

@louwritznel3816 6 лет назад

he probably just uses a pen

@davidd7327 11 лет назад

I have the worst calculus teacher ever!!! Thumbs up:)

@Visiorex 12 лет назад

Let's make a table here... let's make a TABLE.

@benv4 14 лет назад

watch video 2 if u didnt understand where he got t = sqrt (10) :P

@Dotachin2 12 лет назад

does anyone know the program he uses to draw the diagrams?

@justjoua 11 лет назад

I'm taking Calculus right now but I'm having a lot of trouble because m teacher isn't very helpful.. She is mostly a verbal teacher and it's really hard. To be honest this video didn't really help me either )':