Finding Areas in Polar Coordinates

Finding Areas in Polar Coordinates - In this video I show the formula and do a basic example of find areas in polar coordinates.

[itsKyyyle]

To everyone asking why he took half of sin squared: it is the FORMULA for finding the area of a polar curve. You take the integral of 1/2 r^2, r being your function of theta. If the equation is r = cos theta you would do the integral of 1/2 cos^2 theta. If you graph the trig function as a function of x it helps to see where its maximums, zeros, and minimums occur and where it's increasing and decreasing. Since sin has a period of 2pi, sin of 4theta has a period of pi/2, with a maximum value occurring at pi/8 (sin would normally have a maximum value of 1 at pi/2 but since it's sin4theta everything happens 4 times faster). If you don't get that, just make a value chart, pick values of theta to get your r and graph the thing, stop after you finish one loop and figure out what angle interval it is

[Marty]

You're one of the few people that knows this stuff very well and can explain it in a way everyone understands.

Good job, man.

[joshvanselow]

this guy should receive the BRObel Prize

[joshvanselow]

Someday when I'm a successful engineer I'm going to send you money.

[revolutionaryfrog]

I have watched more than 20 videos on this topic and asked my professor and none of them know how to explain how to find the limits of integration or even attempt to explain it. Thank the heavens for this video and this teacher. Thank you so much.

[milindbebarta]

I saw Josh's comment and it's a great idea. After I graduate and get a job, I am going to send you money. Thanks for helping us all. You saved my life.

[timcschott]

twas the eve of the eve of the calculus bc exam...

[nidansandan]

Totally just learned everything I need to know about Conics and Polar calc from your videos. Which is nice, because I have a test in 20 minutes. Pure. God. Lifesaver.

[dr.kennethspeers]

We want to find the area in ONE loop of the graph (in the instructions). If you plot points you will see exactly why he chose 0 and pi/4. He was just making an argument that each time sin (4theta) = 0 we will have gone through one loop of the graph. If you go further to 2(pi)/4 you will see that we make a second loop etc...Hope that helps.

[ekatlo]

misanthropic or not, your contribution towards students around the world is not only globally renown, but globally respected. I studied abroad in the middle east for 2 semesters, and I can tell you that you were watched there. As thousands have said before me: Thank you.

[furkanozturk]

8 years later and you are still saving lives.

[sarakitdotcom]

Thanks so much Patrick. I feel somewhat ok about taking my final tomorrow thanks to your vids. I've understood more in these past few days than I did all semester! If I pass my calc 2 class, it's all thanks to you!! Really do appreciate all your hard work!!

[greasyJFrancis]

I have a great math teacher this semester, seriously top notch, unlike most commenters on here. but these vids have helped me a lot in seeing the material and steps again, sometimes with slightly different techniques from what I learned in class. I like your straightforward style of teaching. very useful stuff. I've sent links to these vids to other students in my class as well. unlike most people I love math, but I still need help sometimes and these vids have been the help I've needed.

[Gilster]

@patrickJMT Please don't take it in the wrong way I didn't mean anything bad by it. I really love your videos. You quite literally have been my professor for my calc 2 class. My prof is horrible. I know people complain about their mediocre profs but you have no idea how bad mine is. He talks like the guy from the clear eyes commercial, he writes directly in front of him so we cant see what hes doing, and he talks to the board as he teaches. I really appreciate all your videos. Thanks A LOT!

[patrickjmt]

@fizzo68 spread the word about the videos is the best 'thank you' i can get!

[patrickjmt]

@EnchantedEnchantress glad you like the videos : ) thanks for the kind words!

[risebad]

dude, no joke you're awesome. this video is 10 times more powerful then hastily taken notes in class. if i get confused a can just come back and watch it again as reference :D

[RuthNPC]

amazing. I *NEVER* understood how to find the angle theta of a problem like this until today. Thank you, thank you, thank you!!

[JonaGman]

What's up Patrick, Its taking me much longer to get through a single one of your videos because I find myself pausing it, getting up, and doing a little dance every time I understand something better. Shoot, I almost did a head spin when you cleared up how to find the limits of integration. I was killing myself over this. U the man!

[patrickjmt]

@DrunkinHulk spring break was last week!