Parametric Equations Introduction, Eliminating The Paremeter t, Graphing Plane Curves, Precalculus
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- Опубликовано: 10 фев 2025
- This precalculus video provides a basic introduction into parametric equations. It explains the process of eliminating the parameter t to get a rectangular equation of y in terms of an x variable. It also discusses how to graph plane curves which is the same as graphing parametric equations. This video is useful for high school and college students taking precalculus or calculus 2. This video contains plenty of examples and practice problems including parametric equations that contain trigonometry such as sine and cosine functions which leads to the graphs of conic sections such as circles and ellipses.
Parametric Equations - Introduction: • Parametric Equations I...
Derivatives of Parametric Functions:
• Derivatives of Paramet...
Tangent Lines of Parametric Curves:
• Tangent Lines of Param...
2nd Derivative - Parametric Equations:
• Second Derivatives of ...
3rd Derivative of Parametric Curves:
• Differentiation of Par...
___________________________________
Horizontal & Vertical Tangent Lines:
• Horizontal Tangent Lin...
Area of Parametric Curves:
• Area of Parametric Curves
Arc Length of Parametric Curves:
• Arc Length of Parametr...
Surface Area of Parametric Curves:
• Surface Area of Revolu...
Polar Coordinates - Introduction:
• Polar Coordinates Basi...
Tangent Line Equations - Polar Form:
• Tangent Line Equations...
____________________________________
Horizontal & Vertical Tangents - Polar:
• Horizontal Tangent Lin...
Area of Polar Curves:
• Finding Area In Polar ...
Area Between Polar Curves:
• Finding Area Bounded B...
Arc Length of Polar Curves:
• Arc Length of Polar Cu...
Surface Area of Polar Curves:
• Surface Area of Revolu...
_______________________________________
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You got a begineer video explaining what paramatization even is? Im in calc and they getting us to do these questions relationed to finding a line and a slope using t as a parameter. I've literally never learnt anything about parametric or paramatization before so yeah.
You’ve got me through cal1,cal2,DE, and now cal 3. Thank you so much sir. Doing the lords work
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@@crow1628 does he have de videos too?
im on the same journey, so far he has gotten me through algebra,pre calc, and trig. hopefully within a year from now ill be done with calc 3
Yup, personally he helped me get through Precalc, Mechanics, Diff. Calc, and Integral Calc.; I will probably use his videos to teach myself for Electromagnetics and Vector Calc./Linear Algebra as well
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In other lectures there is usually a lot of assumed knowledge involved. Which makes sense since this is not low level math, but for someone like me who struggles with adding fractions but is in precalc your videos somehow make it all make sense. It is like MAGIC. Your videos almost always answer every question I have lingering before I have to google or mathway. I am so excited to be understanding math for the first time in my life, its EUPHORIC. Thank you times a million, yeehaw
you struggle with adding fractions in pre-calc? hoe fdid you get this far lol that's crazy. Also there is in now way THIS is in pre-calc, is that what you're saying?
@@ultimatekenz low iq
@@ultimatekenz I have this in pre-calc 2
@@ultimatekenzI have this in precalc 1 as in a sophomore in high school
@@ultimatekenzi know ppl in calculus who couldn’t handle fractions to save their lives
These types of videos with tutoring always have the most positive comments sections its crazy!
hehelloworld123 not always lol
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Bro , this teacher is SAVAGE , he doesnt deserve a single bad word
Well, it's probably full of caffeinated highschoolers doing h.w. at 2 a.m.
@@jamesdanner9854 Lmaoo, that may or may not be me right now
This is helpful af, but I'm still about to fail this cal 2 exam. Pour one out for me bois.
If you tell yourself you're going to inevitably fail an exam it's because you either didn't study enough or you don't have confidence in yourself, gotta believe in yourself and put in the work bro
@@PepsimVideos true I mean studies(from my psych class, sorry no source yet) show, if you say your going to fail, you will be at least 2* more likely to fail
im in the same sinking boat 9 months later, feels bad man
It’s poured my bro.
so did you failedededed?
Learned everything I needed to know about parametric curves within the first 10 minutes. My professor has been teaching this subject for a week now and we had a quiz on it, the class average was about a 70ish percent, I got a 94 and before I watched this video I barely know anything about this, had I not watched this as I was frantically studying before the quiz, I would have guaranteed failed it. Thank you so much.
Bro, you are actually the smartest person alive. Wtf. You have so many videos on so many different topics and they are all taught so well. I wish you were my teacher lol
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Professor Organic Chemistry Tutor, thank you for a positive introduction to Parametric Equations. This is a well-known process of eliminating t in order to get y in terms of x. This material is introduced again in Calculus II and Calculus III. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
I like how he provides a lot of examples to practice and explain. It really helps.
I missed a class and we just started to cover this. With this I feel more confident once I go back so thank you!
Same exact thing I’m going through lol
@@benberkson4481same here lmao
Me rn
Who came here cuz you didn't understand a single word spoken by the teacher during the lecture?
my online coursework is doing a crap job at teaching these things. i learn by understanding what it is and why first not a series of IF/THEN statements to memorize... sucks because conceptually i thought this would be easy to learn. but the programs teaching methodology is so inefficient and backward im often having to do what i did BEFORE coming to school which was to scrape together an understanding through free content. maybe this online format just isnt for me, maybe its just a bad version being used. it would be alright if it was more thorough but personally, Im thinking just need a professor i can get clarification from as concepts are being introduced. I wish you all luck with your coursework friend!
@@freecake1 cheers mate
i come here because i dont go to the lectures lol
some teachers make it so complicated like seriously not that complicated...?
Well
Nobody:
Me right before my exam:
30 minute video I only got 20 minutes
*whips out x2 speed*
SAMEEE
Same.
You’ve helped me through Calc, Calc2, Calc3, Calc4, Calc5, Calc6, and Calc7!!! Not even gonna mention DE 1-12!!! Thank you sooooo much I appreciate it ❤️
im almost done with trig now but hopefully he helps me through calc 1-3 and physics 1-2 lol
calc 7 💀💀💀
bro what are calc4 and onwards. Are those in the imaginary plane or sum
Wth is calc 4, 5, 6, and 7
First day of school and understand nothing about parametric....Thank you!! It really helped!!
You explained in 30 mins what takes me days to figure out. Thanks a bunch fam.
My calc teacher has just been uploading videos for this semester because covid, but I just found out about this channel from a friend and wow this is so much better. Hopefully I can pass this next exam
We're just grateful. Every college student relies on you when their cal exam is like tomorrow!
Great video, thanks! This is so helpful, sir.
A little thought on the problem around 25:00:
x=2^t, y=2^-t. To eliminate the t, we can just say xy=1, and hence, y=1/x.
2^t*2^-t=2^(t-t)=1. So, xy becomes 1. Since both 2^t and 2^-t are not equal to zero, we can divide xy by x, and we get y=1/x.
Man this guy has the most calming voice and he blesses us with this great videos, idk who u r but thanks a lot!
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He teaches math,physics,organic chemistry,general chemistry,biology
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This was straightforward and clear. Thank you so much!
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Probably the most loved creator on youtube
I had a test where I had to convert a parametric equation to a rectangular and I didn’t know how. I swear to god I guessed and did exactly this.
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Thank You 😁 I passed my exams in Calculus
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At 2:48 on the graph, isn't it t=-2 for the leftmost point? rather than t=0?
Riiight? Thank you. I'm not crazy.
I think his brain was on autopilot mode and he just started at zero instead of -2
i also thought that
Sorry. I know I'm late but it should be t = -1 at point (1,1), t = 0 at point (2,0) and so on???
@@pridetrooperjiren548 yes, that's what they mean
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I was really struggling to find a proper lecture on this topic!! Thank you so much !! It was really really helpful!
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at 27:57, there was a simpler way to get y=1/x. like y=2^-t the it also equals to y=1/2^t right, then we replace 2^t with x. we got the y=1/x
omgg ty som much helped me a lot. I was puzzled by the "Eliminating The Paremeter" part but now i know what it means!
this guy can teach anything
You are literally an educational hero. *Thank you* 🙏
Who all is here before a cal 2 exam?
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Thanks
The organic chemistry tutor guys!
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You need to start by defining what a parametric equation IS, why it IS neccessary(if it is so), why and how it came into being. That is an excellent pedagogic method.
John Landon Miller this isn't his first video on the subject
I believe there is a mistake at 2:54, because t-values were -2, -1, 0, 1 and 2. On the graph he started with values 0,1,2,3,4. Am I wrong?
You are right, but it doesn't affect how the graph looks and the directionality. The t values should be from -2 to 2 though
I am here again. Thank you for this video.
i literally learn more in your videos than in my college
lol 13:23 he changes x = 3sint to x = 2sint. Loved the video btw it helped a lot.
nvm i got to where he fixed it lol
You are the reason that I got an A on my midterm
gonna take my calc 2 final tomorrow, wish me luck guys
Great work...years old but still very helpful.
I have a question.... at 2:35-2:44, they said t=0, 1, 2, 3, and 4. wouldn't that be the x values? Isn't t=-2,-1,0,1 and 2? And besides, if t=[0,4] then wouldn't that cross the domain or something?
Samira Tamma yeah he made a mistake. The t value correspond to the coordinates and you choose the direction of lowest to highest from the values where t are
You are right
I was wondering this same thing. I think he made a mistake?
BRO YOU're a legend
You make my life a lot easier
I believe there's an error on the frist graph for the t - they should be from -2 to 2 not 0 to 4
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Thank youu soo much. It was so helpful..❤️
at 5:55 t= 4 not 2 on the uppermost coordinate
2:35 hi can anyone explain to me y he wrote (in green) the r values starting from 0? Because I thought that the points of y he used to plot the graph was from -2 to 2?
He labeled them in order from top to bottom starting at 0 not based on what t actually is , your correct tho, the reason he’s labeling them like that is because he’s tryna show which way the arrows are going but it just makes it more confusing in my opinion you don’t need to label yours when you do them 😅.
"This PreCalculus video", Yeah you better know it forwards and back because in Calculus 2 you will be expected to already know this. Many students are underprepared. PreCalc, can only focus on so much. So some students are here studying it in PreCalc, another majority in Calc 2 wondering where the heck it came from :D
Amazing explanation ❤
Bro I fuckin love this channel. Professors can't teach for shit. (Sometimes)
Gotta get a 78 on my final in two days to pass calc 2. (fingers crossed)
Bro you're a god.
Thank you very much sir
I loved the circle example.
i was actually happy i was understanding it until i made it to the second half of the video
Graphing 0:10
Eliminating parameter 6:10
this is very helpful, now i understand the lesson more. thank you for thiss
thanks bro, my head was about to explode 🤯
What software do you use to write like a board, bro?
Thank you so much!!
MathChris ms paint
15:02 an ambulance went somewhere, I hope that guy is fine
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There's often noises in the background of his videos like ambulances, cars, motorcycles, sometimes even birds chirping! I know this because I've watched like over 600 videos of his. He's a good tutor.
@@Sai1ence agree with that
thank you so much for this, i was about to just throw in the towel and fail my math test
POV: You're running out of time to revise for your maths exam and you know for fact that you ain't passing without this.
A nice teaching.i appreciate
I just got a 100 on my para quiz in precal lets gooooo 🥳I didn’t fucking study I just did my homework I was scared af
Param equations in Pre Calculus? Damn the American education must be falling behind then
@ I mean you’re not wrong lol, but I think that our curriculum is paced that way for AP. AP is international, and now I’m in AP calculus and doing just fine
*His voice comes out
Today we're gonna-
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huhu my brain was out of mind thanks for this!
Your kids are going to be just like you!! Awe
mad helpful thank u brotha
at 2:59 did you mean to put t=-2,-1,0,1 and 2 instead of t=0,1,2,3 and 4
Quick question with the change in base what is the point of changing the Natural log to log if we get the same answer even if we use the natural log?
At 10:25 and even before this, his t values aren't corresponding with the points he plotted.. t = 0, 1, 4, 9 but he uses t = 0, 1, 2.
I don't get it.
I learned more from watching this video ONCE than listening to my "professor" talk for hours. COllege really be a fuckin scam
I'm sorry to say that the notations at 26:44 are all wrong. We never write lnₑ x. ln means log of base e. Also, for a problem like that we just need to multiple the two equations and you simply get xy = 1 and then consider the domain of t to figure out the portion of the curve since in this case t >= 0. It probably takes couple of minutes to do all these. Some of my students follow the method in this video and consequently lost much time and ended up with a low score. At 2:36, it should be t = -2, ..., t=2. I guess it is a mistake. Some of other videos are good, but this problem sends students in the wrong direction. Thank you.
Not an insult. But that may be the difference between someone know math and someone doesn't know the real deal.
Thank you for pointing that out. I had the same question, but didn't know what went wrong.
Yes, why don't you just multiply to get xy=1. Am I wrong here?
@@apiape1206 Yes, you are correct.
It is not a mistake. He list wrong t values for all the problems. Please check one with x sqrt(t).
I think you made a mistake at 2:46. Shouldn't t be between -2 and 2? You have written that t=3 and t=4 at the two rightmost points.
Superb stuff! Keep it up!
Very helpful🤗
all these comments talking about how this video got them thru Calc II or Calc III while my teacher is out here teaching this in precalc :/
Facts but so glad I got to learn this in precalc because i got to understand more in both calc II, calc III, and even physics
Thank you❤️❤️❤️❤️❤️❤️
13:06 x=3sin(t) is changed to x=2sin(t)
nvm he caught it, i should have just watched a little bit further
Thank you 😭♥️
Hello.
May I ask why, specifically, the trig ID was used, at 11:40? I am lost at this point.
maybe a little late but that is because you are trying to get rid of the sin and cos so you set the parametric equations equal to sin and equal to cos then you can use the identity to solve to find the x and y equation.
I'm cooked bro
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Twin
Same...
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Same