Polar Coordinates - The Basics 

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

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

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

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.

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.

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

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 :)

my man summarized a 3 hour lecture in 10 minutes

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.

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

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 RU-vid. But I'm so glad that I am on RU-vid 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.

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

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!

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!

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

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 :)

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.

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.

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

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.

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

Your videos are the only ones worth liking on RU-vid

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

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!!!

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

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

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

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

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

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

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

@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.

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

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

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

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

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!

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

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

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

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

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

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

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

Saving my life in my Multidimensional Math Course

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.

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

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! =]

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

@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!

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

Finals tomorrow, watching these videos for hours.

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

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

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

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

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

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

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

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

I don't know man, this dude is more clutch than Kahwi in Game 6

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! ('':

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

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 :)

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.

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

Thank you, for helping me, to understand polar coordinates better!

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!@!

lol if our teacher just shows us your videos at the beginning of class i bet a ton more ppl would get this stuff, then he/she could just expand on w/e or answer any questions that arise. which is a trip to think about

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)

you deserve the nobel peace prize :)

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.

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

You are the best sir the way you explain is really awesome and from now i am going to refer your videos for maths and i subscribed to your channel.

@whoatonia glad u like them : )

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

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.

absent from school. missed this lesson. enough said thank you

Thanks for the brief intro. Needed a refresher.

Patrick, I have a question. When you plotted (-1, -pi/2), you did the angle first which puts you on the negative y-axis, but then because the -1, is negative, you reflect it over the x, and get the point to be at the positive y-axis. I understand that, but in my math book, there is a problem that says to plot (-6, -pi), so I plotted the angle first which brought me to the positive x-axis, since pi would be the negative x-axis, but then since the -6 is negative I reflected over the y, which would then put the point on the negative x-axis, but in my solutions manual it's placed on the positive x-axis and it wasn't reflected over. So now I am confused. Please help! Thank you.

EXACTLY the answer I was looking for! Thanks.

glad the vids help! good luck in your class!

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

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

not just free, but free and good : )

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.

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

@patrickJMT Khan has quantity but Patrick sure has quality!

@hisyam9 you are very welcome : )

I seriously love you right now

Hey Patrick! I really enjoy your videos, and they're almost always free of errors because you check them so well. I dunno if it's because this video is a bit older or not, but while writing you make a bunch of errors that make it a little more challenging to learn. Hope this was constructive? I'll specify in a reply.

WOW, i never used much of these, only in calc II. Good review, and explained very well :) PatrickJMT, your a buddy to all of us! Keep ROCKING \m/

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

thanks, your videos really do help to understand maths!

Man you make maths to look as easy as ABC

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

By now, I think your question should be answered, but if not allow me to explain. We all can agree that the co-ordinate is past 180 degrees. We can illustrate 180 degrees as Pi. The leftover degrees is 60 and that is Pi/3. Therefore, Pi+Pi/3 = 4Pi/3 (e.g. 1+1/3=4/3)

Use special triangles. it just so happens that a triangle with hypotneuse of 2, opposite of root 3 and adjacent of 1 has an angle of pi/3, now since you've gone 1 pi co-ordinates already in the plot, you add pi/3 to pi, that'll give you 4/3 Pi

my calculator is giving tan inverse of sqrt 3=1/3 pi how did you get 4pi/3 as the final answer can you please help me out

you are very welcome