Graphing a Polar Curve - Part 1 

7 years later and your video is still saving lives

thank you SO MUCH for showing the two graphs and drawing the bottom based off the top, it explains every question i had from my class. youre the best man. best of luck to all who have exams tomorrow.

The period of the curve is equal to (2pi) divided by the integer in front of theta so for... r = 4 sin(3theta) the period is determined by... (2pi)/3 Or in the example above... (2pi)/2 (because it was cos(2theta)) so the period is pi Once you know the period, you just divide by four to get the zero's, crest, and trough. Hope this helps.

this video was posted exactly 10 years ago today and it's still helping me with my class...wow, thank you

glad i was able to help, cesar! thanks for the kind words!!

10 years later and it still so useful. GREAT JOB

I found your videos last night -before 2 days of my calculus exam- and I've been watching you for 5 hours. In the last exam curve was 55 and I got 41:( I hope your amazing videos help me. You are becoming my math god. Muchmuch love and hugs from Turkey.

Who Else came here because their final is tomorrow?

well, this helps me to decide how i label units on the x-axis

When he did 2theta=pi/2 to find the increments, can I do that for every situation or is it restricted to cosine functions?

no matter how old these videos get, patrick will continue making money for years ahead because there's a continuation of people who will take these classes.. go patrick $$$$

This is the first video I've watched where you were somewhat vague on your explanations, especially while beginning to graph. Still better than my professor but I had to watch it a few times

Thank you sir I want to give you 1000000000000000000 likes You are a genius man

The structure plotted is really elegant and just, beautiful.

hey bro, guess what?!...you are the best =D

Dude, thank you so much. My first year calc final is in 3 hours. I've been studying this stuff all night and our teacher didn't teach us any of the polar coordinate stuff. And then he told us it will be on the exam! Ouch! Saved my day super(math)man. Much appreciated.

@Thunder7messiFan come back next semester and tell your friends! : )

you're the best, you're the only reason i'm passing math...

When he is translating his reference graph to a polar one, why does he have r in the y axis and theta in x axis? I though polar coordinates are expressed by (r, theta)

I think because it's the quarter point of the original function, y=cos(theta). To get the period, you take 2(pi)/b from the equation, y=a+b cos c(theta). Then you divide the period by 4 to get the quarter points.

I fucking love this guy. Bro I love you

Even though I think my professor is the best, you did gave a better and more complete example. Thanks for spreading the knowledge !

@tajuara100 why wouldnt they? this stuff has to get paid for somehow. and: you are welcome

should the second graph have x y axis instead of r theta?

God bless you Patrick. you are making lives better with your videos. thank you soooo much!

You explained that way better than my calc professor. Thank you!!!

it's like as soon as i open ur videos i know everything about that topic automatically! :D yay!!!

I'm really glad I watched this, I having been having issues coming up with the increments for pie, and my Uni. doesn't allow any form of calculator. Thumbs up to you

@annie2198 you take the tests, not me : ) so u r the reason!

thank you really cleared up my confusion with graphing outside range given when you have a negative r value.

Excelent!!! it really helps!! and I should say, it's so well explained that even a guy who doesn't speak english THAT well (Me for example) understands!! that's just great!!

thank you i got confused with the two theta. But after your video very thing clicks. Thank You

no problem

question though.. why did you chose to equal the 2Theta to Pi/2?

@patrickJMT YES! Why 2theta =pi/2 Why Not 2theta=2pi (Since that is the Period of Sine)??? Your answer will clear many mind who don't dare to Ask... Thanks

Very nice explaination, really helped! but there's one thing... i believe your second graph should be an y-x graph no?

Very Nice patrick, i appreciate your help and you are sooooooooo talented. i would say be a scientist.

Now i can skip classes and study this at home... And also spend less money with transport 'till College + food. Haha, thanks for posting this Patrick.

he set r=0 so 3cos(2theta)=0, divide by 3, you get cos(2theta)=0 then you want to solve that sooooo when is cos zero? At pi/2 so set 2theta=pi/2 and solve

SO helpful omg i think you saved my math grade.

Hello there Mr.patrickJMT... thanks for the very informative videos!I'll be taking my finals today.so if this will be helpful I will introduce it to my friends to help us on our math problems...keep posting those Informative videos!! take care ciao

You're the best. I've become evangelical about your videos, even though I'm not religious or very social.

Dude! You just made two years of confusion completely disappear in 6 minutes?! *hands you an internet pb and j sandwich*

That's great. I hope this gets more likes because alot of people asked and you actually answered it

@jasskarn666 i could not eat the whole thing

To those who don't know why he set it to Pi/2, try going to fooplot(.)com and see what happens to the graph of y = cos(b*theta) when you change b from 1 to 2 to 3 to 4 until you get it. :)

Awesome tomorrow i have an exam calc 2 and you help me Liked favorite

try and find out

Hi Patrick, your videos are very good, however I am curious on how you consider negative values of r. Surley becuase r=(x^2+y^2)^1/2 makes real negative values for r impossible. This would also have an impact on your plot of r=3cos(2'theta') auggesting that it is undefined in regions such as Pi/4 - 3Pi/4.

Your videos are awesome, thank you for posting them!!!

No, because the angle theta is Pi or 180 degrees, you still just need to go 3 units in that direction.

You are incredible, thank you so much for your videos. I am very grateful.

why are you graphing in the different quadrants for each segment? do you follow it ccw? you just said "now we should be in this section so.." and i understand the negative, but i dont know why you pick the quadrant in the first place

Awesome vid man...before this i was plugging/chugging values of theta(such a waste of time)...but how would i do the same thing if the polar was a lemniscate? it has an "r^2"

You are amazing Patrick

from Pi/4 to Pi/2, why does the line extend to negative r axis and not the negative extended part of Pi/4 angle line

dude patrick ur the best

Now this makes sense. You are a great teacher =)

So i almost got the idea, however, I can't seem to figure out the difference between the first graph and the second one? I mean what are they called?

in your graph isnt the vertical axis suppose to be theta and the horizontal axis r?

at 03:50 why did u plot it on X-axis and then later at 05:17 you plotted it on Y-axis ??

thank you someone should pay you you are a giant help!

on the second point of your graph. how do you know you go -3 down not -3 to the left?!

why are both plots labeled r on y axis and theta on x shouldn't the second one be just the x and y axis

So as a general rule are you always dividing by 2 to get the intervals for your graph, or was it just in this case?

@patrickJMT I'd like to know the answer for the above question also. would u mind explaining it to me plz? Do we always set it equal to pi/2 or it depends? I'm really confused about this. and the fact is that me prof never explained me how to find this. all he did was: cos(2theta) => period = Pi? Thanks in advance!

You are THE man. Seriously, thank you.

Was the last point plotted correctly? I think the radius is 3, but he plots it as r=0. Isnt it?

Yes, I couldn't agree more. SUPER(MATH)MAN = PATRICK

question: im having a hard time how to graph x= 3-cos theta, y= 2+ sin theta do you have any idea how to do it? because i know how to graph when r= but this one is s & y.. thanks!

@patrickJMT so if it was r= sin theta/2..would the increment`s be pi? cuz you would divide theta/2 by theta/2?

should i always set it equal to pi/2 to find the increments? or does that only apply for this problem??!?!?!?!?!

Does anyone know why Patrick graphed in the theta-r plane instead of the r-theta plane? Like if the points are analogous to (x,y) and he chose points for theta, then the points should be (theta,r). But then why have we been graphing polar coordinates as (r, theta) this whole time

Does this method work for graphing other polar functions such as lemniscates and limacons?

Do you always use pi/2 to find the increment?

Honestly, I owe my grade to you Patrick. Thank you VERY much, If I become rich one day, I will keep you in mind :)

top graph: theta = horizontal input r = vertical out put points represented as (r,theta) bottom graph: theta = vertical input r = horizontal output points represented as (r,theta) ?

when you solve for theta at the beginning why do you set your equation equal to PI/2

This is seriously the hardest concept I have come across in calc.... 🤯

i think that theta should be denoted by y axis & r as x axis

I have a final tomorrow and this video just saved me 10% of my exam marks.

shouldn't the left polar point be (-3,pi)?

Thank you Sir.

will it work for cardioids and limacons if you set the inside function equal to pi/2??

So, finding the increment for any polar curve I have to take pi/2 or i can take any other values too? pls reply. Got exam on 13

ha, very nice!

sir I play your videos at 1.5 speed and then it'll be exactly at the rate of how my math prof teaches. point im trying to make: thanks for the great pacing, I can't keep up with my math prof

Thanks! this was a great help

you are a life saver man ,, thanks

patrickJMT chose to put them their himself. He has what is called a partnership with youtube. He gets money for "monetizing" his videos. Just wanted to give you the truth. I don't blame him! Money is money. :) Nonetheless, good videos.

on the LHS of theta axis it's supposed to be -ve ryt? but in the video u plotted (3,π) on the LHS..why?

@achironis10 i mean would you divide theta/2 by pi over 2 giving you pi for the increments?

i think you have to know multiple methods to plot these polar curves i dont think there is one best way...

this is really helpful, thank you

This just saved my life

i watched these this video and didnt go to class for weeks and still passed =]]

thank you teacher... form the begining of semester i couldn't graph well but now .. :)

This video is amazing!

shouldn't it equal pi when you do 2theta = pi/2?

wouldnt it be x=3cos(2theta) anyways? not y=3cos(2theta)