Polar Coordinates - The Basics

Polar Coordinates - The Basics Explained
Description:
Polar coordinates provide a unique way of representing points in the plane, different from the traditional Cartesian system. In this video, we explore the essentials of polar coordinates, from understanding how to plot polar points to converting between polar and Cartesian coordinate systems. We walk through the derivation of important formulas, such as x = r cosθ and y = r sinθ, and how they connect the two coordinate systems. You'll also learn how to convert points and equations between Cartesian and polar forms, gaining a deeper understanding of their applications.
Additionally, I demonstrate graphing a polar equation and analyzing the visual differences between polar graphs and their Cartesian counterparts. These skills are vital for deeper topics in trigonometry, precalculus, and calculus, and they provide a foundation for solving problems involving polar curves and equations. Whether you're a student brushing up on polar graphing or someone diving into advanced mathematical concepts, this video will provide clear explanations and step-by-step examples.
If you find my content helpful or simply enjoy learning math through my videos, please don't forget to subscribe, comment, like, and share this video! Spread the word by telling your friends, teachers, or parents about my channel. Your support allows me to continue creating helpful math content!
Patreon: www.patreon.co...
What You Will Learn:
How to graph polar points on the coordinate plane.
Methods to convert between Cartesian and polar coordinates.
Deriving formulas for converting from polar to Cartesian forms.
How to graph polar equations and understand their properties.
#polarcoordinates #cartesiancoordinates #coordinateconversion #graphingpolar #polarform #mathbasics #trigonometry #precalculus #calculusbasics #polargraphing #math #geometry #algebra #convertcoordinates #rtheta #cartesiantopolar #coordinategeometry #mathvideos #mathhelp #patrickJMT

[@thegreatcabbage8374]

Patrick, you are my savior. I took Calc 2 this semester and you guided me through it like some bearded messiah.

[@patrickjmt]

@nothingelsetodo69 people seem to like khanacademy , but come back here for math! :)

[@dawid4920]

I honestly should be paying half of my tuition to you since I learn everything from you.

[@patrickjmt]

+David Biel I'll send an address! Or be a patron on 'patreon'!

[@jpmiele50]

Your the first Math teacher I've seen that actually teaches you how to do a problem. I blew by Calc 1 and 2 because I could learn it from a book. The professors at my school would spend all class deriving a formula we need to know and assign us problems on it without giving an example. I work in the math tutoring center at my school now and I always tell the people coming in to look at your videos. The way you teach a problem works wonders.

[@jpmiele50]

The problem with a lot of people I noticed by tutoring is that they don't have the correct thought process on how to tackle a problem. Most math teachers will just write it out and say this is how it's solved. You actually explain your own thought process which is vital to a lot of students. Where to start a problem seems to be the biggest issue to a lot of kids. I use this approach when learning myself now. For every topic, I write down a list of steps on how to think and compute the problem.

[@brianm8892]

11 years later and this is still a great help. Thank you so much!

[@shadowpal2]

Dude...thank you. You have no idea how much this helps when a freaking teacher at a private school fails to properly teach me making me resort to KZbin. But I'm so glad that I am on KZbin watching your video right now - because this is so simple to understand, so well explained, and just so straightforward. AT A GREAT PACE TOO. I'm going to go on that website now, because this...is best as it can get.

[@patrickjmt]

@matics19 yea, i do not do much of the flashy advertising stuff. maybe i should

[@patrickjmt]

there is a donation page on my website (there is a link on my channel) !

[@theartist8835]

Man! Thank you! I watched dozens of videos and nobody could explain it as clear as you did!

[@giroarie123]

I just have to say, thank you SO much! I've struggled this past year with my math teacher because he teaches so abstractly, but you have explained every thing perfectly so that I understand. Thank you so much for making math comprehend able :)

[@aarifnazeer]

I have literally tears in my eyes watching this... All this time I was picked up how bad my Analytical Geometry and calculus was. Even teachers made fun of me... But after watching your videos... Its a miracle how fast ive improved... You made it look so easy for me...... Bless dude bless!

[@diogom7817]

see what's funny is that I don't even trust any other video rather than this guy anymore. If my teacher says something different, I'll doubt it very much haha. Keep it up Patrick. People love you

[@JustinKrump]

Wow someone that teaches that you can actually understand. Calc 1 teacher was Chinese, Calc 2 teacher was Russian... Helped me get through Calc 2 considering i could not understand what he was saying... Thanks

[@quinnfoley410]

Patrick, you are truly a life saver. These videos are the only reason I'm passing my classes. Thanks for the taking the time to make them.

[@MrPat8rat]

find it much easier to move along the x-axis find the given 'r' value first. Then you simply rotate the "line" the stated amount to reach your polar coordinate. For example: in problem b) I would move left 2 coordinates on the x-axis (to get to -2), and then I would rotate the line π/4 units counter clockwise (just as a normal unit circle would rotate) to get to the polar coordinate (2,π/4). Keep up the great work Patrick!!!

[@DollarMoviesUSA]

Usually typing "pi" if you're doing homework or some sort of math program, that program will recognize it. similar to using sqrt() for square root.

[@unknownlove19]

you deserve the nobel peace prize :)

[@Sir_Princely]

Thank you PatrickJMT soo much for sharing your wisdom with the world. It's very well appreciated. Your explanations are rich. Keep up the great work.

[@ekatlo]

you should be proud of your teaching abilities. you have contributed knowledge and relief to many young students. major props.

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Been getting this ad asking if these videos from 5 years ago actually help Screw those ads yes these are

[@mannyman1012]

One day I will learn all your videos and I will conquer the World....for better or worse!

[@Mrius86]

It's funny how I feel like I lose more and more of my grasp of the fundamentals the deeper I go in calc 1. Always so many new things to learn and it's like pushing all the other stuff away. I grow more stupid every day I try to do my math homework. Thank you to PatrickJMT for trying to teach me mathematics :)

[@SecksyMan]

you are a very good teacher. I'm learning on Khan Academy, but he does not have videos on everything. This is a perfect alternative. Thank you very much!

[@patrickjmt]

my videos are better :)

[@kimchangjoon]

I think so, too.

[@mortadaal-khateeb319]

Thank you very Much , as a civil engineering student who have been out class all the time , This helped more than I was gonna deserve.

[@mitcheroni321]

this kind of video deserves a Nobel Peace Prize!!!!!

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Your videos are the only ones worth liking on KZbin

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Bad ass examples man! very well appreciated!

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I am going to pass my final thanks to you!

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i love your handwriting

[@hagriever]

youre a genius, 2nd day and 2nd time actually helping me with my homework, you sir just gained another subscriber

[@hellomyfriend2053]

Thank you so much you taught me more in 10 minutes than my teacher in 2 hours. I will donate as soon as I am old enough to make a pay pal account thanks... Andrew

[@naoahak1888]

you are the best man > I hope u've successful life wish u the best

[@mjavedakbar]

brilliant man, u explain excellently

[@greyalien9292]

On my planet, we use hyper-polar coordinates to calculate 11 dimensional shapes, you humans have a long way to go.

[@elnekosauce]

+Grey Alien Jesus christ, your numbering system must be insane.

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+Grey Alien....we have cat videos....

[@mohammedalialnuaimi6102]

+Andrew Massey hahahahaha that is a good one ahahaha

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we have dank memes

[@ritwikchakraborty3319]

ha you know only 11 dimensions.....how funny....we know 26 dimensions...call Hawking to better suggestion

[@Blueskyaz91]

It's really good, now I got it, thanks for great job

[@morphin3lips]

every time i search for math help... i pray that you have examples! so helpful!!

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my man summarized a 3 hour lecture in 10 minutes

[@silverreyes7912]

Great refresher, thanks

[@GenericCoder]

thanks a lot man for your videos learned a lot from it.

[@andy120692]

You are a great teacher.. Whenever I need some help on my math homework, I just type it in on youtube, and it's there.. Very helpful, very easy to understand, just good overall. Thanks!

[@joshfrary]

Years later and here I am looking up the same videos i did when i was enrolled courses that taught this content... Now prepping for my FE exam and just given ya a shout out! thanks much

[@patrickjmt]

good luck! :)

[@tcarp77]

dude this video was so crucial, you r 5 times better than my math teacher. mad props. 213.

[@TheDanielGraves]

Thank you again, for making a corner of sanity and sense here. You've won the hearts of a million frustrated students

[@TheDavstar1]

Have a test tommorrow, didn't have clue about polar coordinates before, now I do! Thanks heaps man!!!! :D

[@dennyle6050]

wow some good stuffs their Patrick.Thanks

[@kassthatt]

yah seriously helps a lot!! you are helping numerous people!! how to donate

[@EmdozPro]

Earlier in the video, it is shown that Tanθ=x/y. If you take the angle from the dotted line to the negative x axis (i.e. start on the dotted line, and move clockwise until you hit the first line, the negative x axis line), and find that angle (R), it is π/3. You use TanR=O/A, with A=1, and O=√3. Then R=Tan-1( (√3)/1 ), so R=π/3. Then Patrick has taken the positive angle, so he starts from the positive x axis, and moves anti-clockwise until he hits the line, so θ = π+R = π + (π/3) =4π/3

[@Cheedillow]

This was very helpful, I have an FP2 A-Level exam tomorrow and this lays down basics for me..

[@patrickjmt]

ha, back at cha brotha! thanks for looking out for me on the other video in regards to the annotations

[@crieman123454321]

I have a math final and I i'm on the verge of C and D Thanks to you i'm sitting at a C and i'm not going to lose my scholarships! =]

[@Veganphobic]

its the last day before the final and my mind is so tired and I'm having a hard to teaching myself at home (as I've bee doing the entire quarter) so thank you a lot for teaching me... you saved me a lot of stress, and a lot of time

[@janiex7031]

Hi, I'm here 45 minutes before my exam, and Patrick is indeed saving lives everywhere!!! Thank you.

[@patrickjmt]

@matics19 well, i think people find them from a google or youtube search anyways. i am not sure a flashy banner makes any difference. and anyways, i am not a flashy guy. if people watch, that is fine. if not, that is fine too!

[@d4Nc3rCr4zy]

Honors pre calculus? more like: watch Patrick's videos because your teacher doesn't teach

[@zeinhanouneh6812]

Gr11 over here and I'm taking this.

[@blackoutgenez]

where are you from

[@d4Nc3rCr4zy]

blackoutgenez I'm from socal. I'm a junior now and taking ap calc BC

[@georgeabreu6392]

d4Nc3rCr4zy How was the AP exam?

[@d4Nc3rCr4zy]

George Abreu I think I have PTSD from the frq's....

[@12Alforja]

Patrick no one, but one million of thanks for a wonderful video and so helpful. God bless you Patrick. Thanks

[@mza131313]

you saved me 30 mins before my math 150 test. many thanks

[@saronghezai]

You have been nothing but my "Math Angel". Helen

[@patrickjmt]

@whoatonia glad u like them : )

[@arielartista93]

Patrick, I LOVE your videos, but they make me overly confident for the exam. xD You give very doable problems and it is easy to understand, but then my professor will give a problem that's 10x as hard. Could you post really challenging problems as well? Thanks! Great video, though.

[@patrickjmt]

well this video is entitled 'polar coordinates - the basics' and not 'polar coordinates - the hardest problems ever' !

[@arielartista93]

Touche..

[@lucky-wq5yx]

+arielartista i'm 2 years late but daaaamn. #triggered

[@zain4019]

I think Patrick makes these videos for two reasons- to help others and also to leave sassy replies.

[@fatihpehlivan6034]

Did you handle the professor?

[@megangutman1932]

You seriously save my life when I miss a lecture. Thank you!

[@hisyam9]

Dude you rocks man!! I hated them in my first year but now you made me love them.. You made is sound SO EASY.. Thanks a lot dude

[@AmberinTrees]

thank you so much!!! since i've watched your videos, my grades have improved. some people just can't teach math- like my TA!!

[@emmanuelidiku2983]

after watching this, am like. why is this so easy? but then again your explanation does a lot to make it easy thanks man

[@patrickjmt]

not just free, but free and good : )

[@JamesTBond]

Have a midterm on Monday and these videos are really helping. :)

[@chrissizkool]

dude..do you know how awesome you are. You can be the pivotal decision between a C and a B in cal 2. Im an njit student and a math major, and njit is ranked 10th in nation for best math courses.

[@richardcandia7811]

learned more in these 10 minutes than a week in class. thank you my good sir.

[@patrickjmt]

you are very welcome

[@charlotte8060]

this is the best explanation i found on the basics of polar coordinates!! Thank you so frikken much, this just saved my IB Math lab report :)

[@KevC126]

Saving my life in my Multidimensional Math Course

[@AfroQueenB]

I remember when logs were just things in the forest. I remember when "e" was only part of English class. Life made sense. Then I started calc. I remember my first test (70). I remember when I didn't know about Patrick and calculus was impossible, that was a dark dark time.

[@jasonpfau1377]

Nice video. You really help more than my teacher, which is not a surprise.

[@patrickjmt]

no problem

[@patrickjmt]

glad the vids help! good luck in your class!

[@richamandsaurwale1619]

@Andrew Lee at 8:40 if you remember the unit circle, then at 240 degrees, Sin(x) equals -root 3/ 2 and Cos(x) = -1/2. Sin(x)/ Cos(x) = tan(x), so (-root 3/ 2)/ (-1/2) = simply root 3, which is 4 pi/ 3. I was having difficulty with this problem too until I realized that it simply uses the basics of the unit circle.

[@letsrockroll]

Thanks very helpful.... you should be a math teacher. My high school needs a guy like your.

[@RayHigaJumba2]

Thank you so much Patrick, You have helped me thoroughly with Math, allowing me to get high marks on all of my tests and assignments, thank you!@!

[@martmelee]

dude i love you!!! xD once i get done with my engineering, i will probably study mathematics. i love math but sometimes it gets harder, but i think that's what i like about it lol.

[@Zerog65]

these videos are a great help. You help to explain everything very well alot better than most teachers I have had. I know this is probably dumb to ask but the integral of x*e^x^2 alway give me trouble remembering any help anyone.

[@mariamakematoure]

I seriously love you right now

[@Carlos2312]

Oh god.... You don't know how thankful I am to stumbleupon to have found your website. THANK YOU FOR ALL THIS VIDEOS. Now understanding double and tripple integration is possible and I'll pass Calculus III. Than you! ('':

[@aadrossart]

Finals tomorrow, watching these videos for hours.

[@nothingelsetodo69]

so guys, do you know a channel as epic as patrick that explains physics? That would be great

[@stamaxo]

Finally makes sense, after my teacher did not talk about negative radius!

[@fahimm90]

thanks a lot man for all the videos , i watched them over the summer and learned more than what i learned in class :D

[@03436200787]

i dont know u but i love u!!! thankyou thankyou thankyou sooooooooooooooo much, i was failing calc and on the last test i got an A..its all U

[@longbeach225]

Thanks man your the best!!! Now I feel more confident about my calculus exam.

[@dvorakfan3]

Very helpful and straight forward! This video correlated exactly with my homework.

[@muffincita5]

@patrickJMT Too accurate! You're the best at explaining everything.

[@kalef1234]

nice thanks man! sometimes just watch your videos to remind my self of things we've already done so I don't forget them for the final

[@t5kcannon1]

Thank you for the video. I have a question: You talk of a negative radius, but some maths books define r >= 0, and undefined, and exclude the possibility of r

[@JayBird1031]

Thanks so much for a well-rounded clear explanation, Patrick! This greatly helped!

[@dylanparker130]

when you're doing the (a - c) examples of polar coordinates, it may help if you said (apologies if you did) that all of these are not of the form (x,y) but (r,theta), i.e. polar form is (r,theta)

[@TheIcthyosaur]

Thanks for the brief intro. Needed a refresher.

[@mightylimau]

i don't have a further math teacher in my school so thank you so much for the video. may god bless you :)

[@patrickjmt]

@SuperSmarty7 the square root of 4 is 2.

[@clairejones314]

EXACTLY the answer I was looking for! Thanks.

[@ajr293]

thanks so much! this really helped me prepare for my test tommorow (:

[@V0r4c105wyv3rn]

Thank you for the video. You saved me from crashing and burning on my quiz.