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.
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 $$$$
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.
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
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.
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!!
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
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.
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
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)
When you solve a function you are usually solving for 'y'. When we solve for polar coordinates we are usually given them as a function of 'r', where 'r' is the distance away from the origin or the length of the segment. The theta shows at which angle that 'r' value moves.
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
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
@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!
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.
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!
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"
@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
+fares223 In a polar set of axes, there is no radius axis! If a radius axis was present, we would need to take component of a line along 'x-axis' and do all sorts of complicated shizz. A polar set of axes only has theta and radius axis is more like a circle (a locus of all point equidistant from origin).
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
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. :)
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
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.
7 years later and your video is still saving lives
make that 9 years!!
@김진욱 Soon it'll be 11!
@@matinnawabi3912 oooh I cant wait!!
11 years now!
12 years lol
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.
glad i was able to help, cesar!
thanks for the kind words!!
this video was posted exactly 10 years ago today and it's still helping me with my class...wow, thank you
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.
10 years later and it still so useful. GREAT JOB
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 $$$$
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.
well, this helps me to decide how i label units on the x-axis
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
When he did 2theta=pi/2 to find the increments, can I do that for every situation or is it restricted to cosine functions?
you're the best, you're the only reason i'm passing math...
The structure plotted is really elegant and just, beautiful.
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.
how was the test
Even though I think my professor is the best, you did gave a better and more complete example. Thanks for spreading the knowledge !
it's like as soon as i open ur videos i know everything about that topic automatically! :D yay!!!
Thank you sir
I want to give you 1000000000000000000 likes
You are a genius man
hey bro, guess what?!...you are the best =D
That's great. I hope this gets more likes because alot of people asked and you actually answered it
Who Else came here because their final is tomorrow?
+Aninda Halder me!! I will take my Final later
Me
me rofl my short answer portion is tomorrow, and multiple choice is in 4 days
Goodluck!
Thankss
Dude! You just made two years of confusion completely disappear in 6 minutes?! *hands you an internet pb and j sandwich*
You explained that way better than my calc professor. Thank you!!!
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!!
@tajuara100 why wouldnt they? this stuff has to get paid for somehow. and: you are welcome
God bless you Patrick. you are making lives better with your videos. thank you soooo much!
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!
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.
SO helpful omg i think you saved my math grade.
@jasskarn666 i could not eat the whole thing
running out of time on a 6 min video in 2008 meanwhile videos nowadays on youtube can be an hour long...
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.
no problem
should the second graph have x y axis instead of r theta?
@achironis10 i mean would you divide theta/2 by pi over 2 giving you pi for the increments?
Very Nice patrick, i appreciate your help and you are sooooooooo talented. i would say be a scientist.
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
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)
Was just a reference to see when the radius is increasing or decreasing.
When you solve a function you are usually solving for 'y'. When we solve for polar coordinates we are usually given them as a function of 'r', where 'r' is the distance away from the origin or the length of the segment. The theta shows at which angle that 'r' value moves.
that confused me
Its the jacobian determinant when going from cartesian to polar form
at 03:50 why did u plot it on X-axis and then later at 05:17 you plotted it on Y-axis ??
Your videos are awesome, thank you for posting them!!!
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
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 are incredible, thank you so much for your videos. I am very grateful.
thank you someone should pay you you are a giant help!
You're the best. I've become evangelical about your videos, even though I'm not religious or very social.
I have a final tomorrow and this video just saved me 10% of my exam marks.
@Thunder7messiFan come back next semester and tell your friends! : )
@patrickJMT so if it was r= sin theta/2..would the increment`s be pi? cuz you would divide theta/2 by theta/2?
You are amazing Patrick
thank you i got confused with the two theta. But after your video very thing clicks. Thank You
will it work for cardioids and limacons if you set the inside function equal to pi/2??
@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!
Does this method work for graphing other polar functions such as lemniscates and limacons?
You are THE man. Seriously, thank you.
question though.. why did you chose to equal the 2Theta to Pi/2?
+Broke noob I mean why Pi/2 specifically?
HUHUHUHU ^^^
I was wondering the same thing, shame that Patrick always seem to fail to explain critical points of some concepts.
omg i understood it 2 months ago and i would tell you the answer but i forgot how to do this
I thought he was using that as an arbitrary, example angle showing how he was going to plug in angles and obtain values for 'r'.
Now this makes sense. You are a great teacher =)
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.
Very nice explaination, really helped!
but there's one thing... i believe your second graph should be an y-x graph no?
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?
Awesome tomorrow i have an exam calc 2 and you help me
Liked favorite
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!
Do you always use pi/2 to find the increment?
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"
dude patrick ur the best
should i always set it equal to pi/2 to find the increments? or does that only apply for this problem??!?!?!?!?!
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
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
@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
Honestly, I owe my grade to you Patrick. Thank you VERY much, If I become rich one day, I will keep you in mind :)
This just saved my life
in your graph isnt the vertical axis suppose to be theta and the horizontal axis r?
6:25 I think the theta-axis should be replaced with r-axis and vice versa because he said that the point is (3, pi)..Right?!!
Can any one answer me ??
Well said!
+fares223 In a polar set of axes, there is no radius axis!
If a radius axis was present, we would need to take component of a line along 'x-axis' and do all sorts of complicated shizz.
A polar set of axes only has theta and radius axis is more like a circle (a locus of all point equidistant from origin).
I fucking love this guy. Bro I love you
Be HUMBLE!
ha, very nice!
on the second point of your graph. how do you know you go -3 down not -3 to the left?!
try and find out
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?
Can this work for any plotting of polar curve?
you are a life saver man ,, thanks
wow dude, you just made this fun!
This video is amazing!
thank you teacher...
form the begining of semester i couldn't graph well but now .. :)
can you graph well now?
this is really helpful, thank you
11 years in the future thank you!
i watched these this video and didnt go to class for weeks and still passed =]]
Thanks! this was a great help
You're a hero
shouldn't the left polar point be (-3,pi)?
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
thx, without you I would screw up on my exam
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.... 🤯
don't worry, it only gets better (by which i mean harder) from here :)
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. :)
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
shouldn't it equal pi when you do 2theta = pi/2?
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.
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
Yes, I couldn't agree more.
SUPER(MATH)MAN = PATRICK
Thank you Sir.