Unit Circle Trigonometry - Sin Cos Tan - Radians & Degrees

  Рет қаралды 2,016,495

The Organic Chemistry Tutor

The Organic Chemistry Tutor

8 жыл бұрын

This trigonometry tutorial video explains the unit circle and the basics of how to memorize it. It provides the angles in radians and degrees and shows you how to evaluate sin cos and tan.
Trigonometry - Basic Introduction: • Trigonometry
The Unit Circle:
• The Unit Circle, Basic...
How To Remember The Unit Circle Fast:
• How To Remember The Un...
Reference Angles:
• How To Find The Refere...
The Six Trigonometric Functions:
• The Six Trigonometric ...
How To Solve Right Triangles:
• Trigonometry - How To ...
_____________________________
Reciprocal Identities:
• Reciprocal Identities ...
Quotient Identities:
• Quotient Identities - ...
Even and Odd Trigonometric Identities:
• Even and Odd Trigonome...
Pythagorean Identities:
• Pythagorean Identities...
The Pythagorean Theorem:
• Pythagorean Theorem - ...
Trig Functions - Periodic Properties:
• How To Evaluate Trigon...
________________________________
The Exact Value of Trig Functions:
• How To Find The Exact ...
Special Right Triangles - 30 60 90:
• Special Right Triangle...
Special Patterns - Pythagorean Theorem:
• Special Patterns of th...
Cofunction Identities:
• Cofunction Identities ...
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 747
@TheOrganicChemistryTutor
@TheOrganicChemistryTutor 6 ай бұрын
Final Exams and Video Playlists: www.video-tutor.net/ Trigonometry - Basic Introduction: kzfaq.info/get/bejne/nZ6GdquguNGZj6M.html How To Graph Trig Functions: kzfaq.info/get/bejne/nLeAgqWAq8iWo40.html Evaluating Inverse Trig Functions: kzfaq.info/get/bejne/qdVph82cm63FYok.html Verifying Trigonometric Functions: kzfaq.info/get/bejne/hKtmrcZ7uMDMiGQ.html Trigonometry Final Exam Review: kzfaq.info/get/bejne/haejldtluavSfGQ.html
@creampopz
@creampopz 5 жыл бұрын
I had a test on this today that determines whether I graduate high school or not. Thanks to you, I will be graduating with my class. Thank you so much!!!
@derrick6860
@derrick6860 4 жыл бұрын
Congrats bro!!
@IrvinMenezes
@IrvinMenezes 3 жыл бұрын
WWWW
@santidoesdata5128
@santidoesdata5128 3 жыл бұрын
did u graduate?
@creampopz
@creampopz 3 жыл бұрын
@@santidoesdata5128 i did, in college now
@zambixd7605
@zambixd7605 3 жыл бұрын
@@creampopz iam in grd 9 lol
@taal7245
@taal7245 5 жыл бұрын
this guy always saves me.
@angielapaulino4791
@angielapaulino4791 4 жыл бұрын
Maybe you're meant to be, haha, joke
@o_5553
@o_5553 4 жыл бұрын
same
@ryangraves4961
@ryangraves4961 4 жыл бұрын
In quarantine and I’ve learned more within 6 minutes than my trig teacher has taught me in a year
@wscu2318
@wscu2318 4 жыл бұрын
You don’t know how golden this comment is
@codenameidk206
@codenameidk206 3 жыл бұрын
True
@WahTzH3k
@WahTzH3k 5 жыл бұрын
Almost everyone is here cuz their teacher can't explain for shit LMAO
@ZckxBlckTheTwnGurdins
@ZckxBlckTheTwnGurdins 4 жыл бұрын
ikr
@monke6776
@monke6776 4 жыл бұрын
I’m here because I chose not to pay attention and have a test second period tomorrow
@ZckxBlckTheTwnGurdins
@ZckxBlckTheTwnGurdins 4 жыл бұрын
@Michael Terrell II ✖AMEN 😄👌
@rakotai9998
@rakotai9998 4 жыл бұрын
nah. its just because i want to learn new concepts. Although he is a very good teacher.
@danielcahigas5016
@danielcahigas5016 3 жыл бұрын
REVz our teacher actually sent this tous as our lesson tf
@n0thmed116
@n0thmed116 3 жыл бұрын
21:45 "WhAt aRe YoU dOiNg " I luv this guy.
@GordonRamseyIsMyLifestyle
@GordonRamseyIsMyLifestyle 3 жыл бұрын
lmaoo
@123ericsb
@123ericsb 6 жыл бұрын
Thank you for your videos. I assign your videos to be watched in my precalculus class. I am a very tough teacher, but with your videos combined with my lectures, the lowest grade in my class stands at a 92. I never thought that would be possible. Thank you for all posts.
@Kalliegurl
@Kalliegurl 5 жыл бұрын
I wish my instructor would think this way too lol
@syub2407
@syub2407 4 жыл бұрын
my teacher doesn’t give a shit if we fail lol
@Ivan-se5ge
@Ivan-se5ge 4 жыл бұрын
Aaron Bergante :(
@hopeenvy
@hopeenvy 3 жыл бұрын
You're a great person
@missy3041
@missy3041 2 жыл бұрын
I would be very happy to be in your class’ lowest grade
@BigManTing79
@BigManTing79 3 жыл бұрын
*already struggles to understand math in class* Online Learning: Let me introduce myself
@sherenemichaels4738
@sherenemichaels4738 2 жыл бұрын
The unit circle is just a way of adding 30ths and fifteens to the number that comes immediately before it in order to get the next number After zero we add 30 After 30 we add 15 to get 45 After 60 we add 30 to get 90 After 90 we add 30 to get 120 After 120 we add 30 to get150 after 150 we add 30 to get180 After 180 we add 30 to het 210 After 240 we add 30 to get 270 After 270 we add 30 to get 300 After 300 we add 30 to get 330 After 330 we add 30 to get 360 The addition of fifteens comes inbetween The numbers directly before and after 0, 90 180 270. We add thirties To all the others we add fifteens 30, 150 210 330 all have sine and cosine coordinates of square roots of three over two and 1/2 ...... In some variations or other depending on which quadrant they are in they may be positive or negative Remember that sine is mapped to the Y axis while cosine is on the X axis ( COSINE, SINE) This way you can learn the unit circle just by adding fifteens and thirties to preceeding numbers to get the current number if you study it a bit Not want to bore you anymore by teaching you many more methods to learn the unit circle I am Richard Michaels Younger brother of Shereen Michaels and I am a student at SUNY in New York USA Cant give out my email address here Too public Would love to help more if I could Sorry
@candycanestripes1305
@candycanestripes1305 6 жыл бұрын
Sir, you are doing a great service to all intellectuals. Please keep going.
@dhasvanth.m.g6572
@dhasvanth.m.g6572 Жыл бұрын
And dumb people who need to get by
@astroh8674
@astroh8674 Жыл бұрын
Whoever had you as a professor... I envy them. Great work and thank you for making this so understandable.
@sanopann1896
@sanopann1896 Жыл бұрын
bro can i ask for help at 32:17 why the negative leave behind in the numerator
@astroh8674
@astroh8674 Жыл бұрын
@@sanopann1896 I’m pretty sure you can’t have a negative numerator ?
@oldHavenNicholsishere
@oldHavenNicholsishere 11 ай бұрын
@@astroh8674 That becomes negative for the entire fraction I think....
@SweatBloodTears
@SweatBloodTears 7 ай бұрын
Had same question @@sanopann1896
@RackUR
@RackUR 3 ай бұрын
@@sanopann1896 The negative can be anywhere, in the numerator, denominator r the middle and it'll be the same result
@meganhamilton8879
@meganhamilton8879 5 жыл бұрын
When your teacher makes no sense but this completely does. Thanks for saving my grade.
@davidharmon8809
@davidharmon8809 4 жыл бұрын
Wow, this video explained more to me in the hour that I watched than my math teacher did explaining the whole unit in 2 weeks, thank you!
@gameswithricky1264
@gameswithricky1264 Жыл бұрын
The fact I was able to memorize the unit circle entirely in 10 minutes with just this video is incredible. Thanks so much
@hi-hc3ms
@hi-hc3ms 11 ай бұрын
you didn’t need to memorise the unit circle 💀.
@gameswithricky1264
@gameswithricky1264 11 ай бұрын
@@hi-hc3ms I needed to cus I wanted to skip algebra 2 and it was the only thing I was unsure about
@ZhiwaJ
@ZhiwaJ 2 ай бұрын
@@hi-hc3msit’s actually very useful for the first and second derivative test for trig functions
@Justsayitsjose
@Justsayitsjose 3 жыл бұрын
I just want to graduate 😭😭😭
@braydenWatz_creates
@braydenWatz_creates 2 ай бұрын
No
@lavalampa2020
@lavalampa2020 2 ай бұрын
Ikr luckily youre done now
@SamudraFlavorsYT
@SamudraFlavorsYT Ай бұрын
How are you
@bread5286
@bread5286 Ай бұрын
Real
@TheNineteenthOfTheFirst
@TheNineteenthOfTheFirst 27 күн бұрын
Real
@mohamedhashim3038
@mohamedhashim3038 5 жыл бұрын
*types tan(90°) in a calculator* calculator: UHMM..I THINK TF NOT
@Kevessi
@Kevessi 5 жыл бұрын
Lmao
@cassied9327
@cassied9327 5 жыл бұрын
😂
@user-fr9ec4xq1e
@user-fr9ec4xq1e 5 жыл бұрын
😭😭😭😭
@DianaLlovitmacam08
@DianaLlovitmacam08 4 жыл бұрын
Commit divide by zero!!
@MohamedAli-zq4xt
@MohamedAli-zq4xt 4 жыл бұрын
@@DianaLlovitmacam08 XD
@waltpires231
@waltpires231 5 жыл бұрын
It's incredible your teaching skills. I love all your videos as they're clearly explained and easy to understand. I can't thank you enough. You're doing a good job. Keep it up.
@durga18991
@durga18991 5 жыл бұрын
For maths hand written notes of graduation maths subscribeRUBEL BHATIA MATHEMATICS.
@ChangedNames
@ChangedNames 4 жыл бұрын
I remember my high school teacher telling us the expression as Add Sugar To Coffee, and then in our senior year he told us it as, All Students To Collage. my favorite teacher tbh he makes math fun
@jordanroos1634
@jordanroos1634 5 жыл бұрын
Thank you so much, I now understand this stuff, I wish teachers and text books would go over every step like you do so we can see and understand how things fit together
@nicohaba2203
@nicohaba2203 Жыл бұрын
thanks so much for this video omg I have had several people try to teach me to understand the unit circle and I never ever get it but this made me understand
@Frank-cb4yv
@Frank-cb4yv 3 жыл бұрын
This dude is so good at explaining! Math is my best subject so when I was struggling in class, I knew it had to be my teacher.
@atakashikiru1304
@atakashikiru1304 3 жыл бұрын
I've always been watching your videos whenever I have math problems and it all help me a lot. THANK YOU VERY MUCH. You're genius!❤
@camilla.callow8
@camilla.callow8 Ай бұрын
I love how I slowly get the material more and more, it's really satisfying. Thank you so much
@mrdarsh1547
@mrdarsh1547 3 ай бұрын
Spent 2 Weeks on this topic and this You tube video made me understand it better and faster then my teacher. THANK YOU
@alumi9818
@alumi9818 4 жыл бұрын
13:40 really important to memorise 23:00 better method is to think about pi/6 instead of 5pi/6 and just multiply it by 5 - so: pi/6 = 30 so 5pi/6 = 150
@mxlxzybbb
@mxlxzybbb Жыл бұрын
Why multiply it by 5???
@yuji3171
@yuji3171 Жыл бұрын
I did sin ( 5pi/6) in my calculator and it does not equal to 1/2
@bigfgreatsword
@bigfgreatsword Жыл бұрын
@@yuji3171 If you are using the 580X Casio, there's a OPTN button, for degree to radians conversion, it's the little r, hope this helps!
@yuji3171
@yuji3171 Жыл бұрын
@@bigfgreatsword thank you so much!
@Phoenix-np1iu
@Phoenix-np1iu 2 ай бұрын
Yeah just remember 0 degrees to 90 degrees and go from there more or less
@krshhv
@krshhv 3 ай бұрын
his voice is my inspiration to continue studying 😄
@iloveshenquanrui
@iloveshenquanrui 21 күн бұрын
REAL
@ranasalih7592
@ranasalih7592 5 жыл бұрын
Thank you very much...I studied trigonometry 10 years ago,now I am studying calculus,with your video I refreshed my memory...God bless you
@moya-gayehamilton1132
@moya-gayehamilton1132 6 жыл бұрын
Wow! All I need to knw abt trig in just 1 hr!!! This is awesome!!! Thnx sooo much!!
@christidel
@christidel 7 жыл бұрын
I cannot thank you enough!!!!!! I would not be passing precalc without you. Really really really appreciate all your videos you explain it clearly
@TheOrganicChemistryTutor
@TheOrganicChemistryTutor 7 жыл бұрын
You're very welcome
@starsighting7167
@starsighting7167 6 жыл бұрын
I freakin hate that class
@durga18991
@durga18991 5 жыл бұрын
@@TheOrganicChemistryTutor for bsc btech msc maths hand written notes follow RUBEL BHATIA MATHEMATICS
@quicks4253
@quicks4253 Жыл бұрын
@@starsighting7167 Hey buddy I loves watching Unit Circle Trigonometry - Sin Cos Tan - Radians & Degrees however when I see comments like this it ruins my day and only ruins this great intellectual community. Please don't disrespect Unit Circle Trigonometry - Sin Cos Tan or any material related to this. Have a great day!!! But don't I hate u
@69feetwide
@69feetwide 6 ай бұрын
@@quicks4253 🤓
@batfaengz
@batfaengz 4 ай бұрын
I can’t even tell you how much this helped. I asked 3 math mentors about it and none of them could explain it to me but I FULLY understand it now. Thank you so much🙏🙏
@AyushKumar-eg1vt
@AyushKumar-eg1vt 2 жыл бұрын
This was so helpful to me, I was consumed by these problems in the class as I was the only one unable to do this and had hesitance to ask the teacher such a basic thing
@CR35C3ND0
@CR35C3ND0 2 жыл бұрын
U have no idea how many people you have helped every second of all of your videos you're a Godsend
@ButterflyColors
@ButterflyColors 3 жыл бұрын
I just want to say thank you to this channel. I don’t understand anything my teachers teach me, it’s ungodly how lost I will be, this guy is the real MVP math teacher here
@iloveshenquanrui
@iloveshenquanrui 21 күн бұрын
i love this dude's videos so much hes a life saver fr
@henrywatts7033
@henrywatts7033 6 жыл бұрын
Thank you, thank you, thank you !!! Now I can see the relationships, rather than learning reference angles in isolation, WOW !!!
@eliahsbambo7016
@eliahsbambo7016 5 жыл бұрын
This is the first time i literally enjoy Trig... Thanks Bro.
@hell0w0-54
@hell0w0-54 2 жыл бұрын
This guy is my educational saviour. The way he simplifies and teaches so effortlessly. Thanks bro!!
@phumelelegumede8813
@phumelelegumede8813 5 жыл бұрын
You just saved my life dude thank you so much!
@vipinsharma9342
@vipinsharma9342 2 жыл бұрын
thanks for clearing the doubt sir. it was the greatest video on trigonometry I have ever seen.
@jeongjeongmusic
@jeongjeongmusic Ай бұрын
watched this in highschool 7 years ago. watched this in college 5 years ago. watching this again as an employed engineer studying for my FE. thanks organic chemistry tutor :D
@EternityMoix
@EternityMoix Жыл бұрын
Better way to memorize this, Sin30 = 1/2 Sin45 = sqrt2/2 Sin60 = sqrt3/2 Cosine is just the opposite, Cos60 = 1/2 Cos45 = sqrt2/2 Cos30 = sqrt3/2. If you look at this the Sin values goes from least to greatest, and Cosine values goes from greatest to least. Regarding Tangent, its just Y (sin) /X (cosine) or Opposite / Adjacent, Tan30 = 1/sqrt3 = sqrt3/3 Tan45 = sqrt2/2 / sqrt2/2 = 1 Tan60 =sqrt3/2 / 1/2 = sqrt3 For reference angles just remember if the given angle is closer to 180 or 360 degrees or Pi / 2pi. When in radians for example if given Cos(2pi/3) you can ignore the 2 and just focus on pi/3 since thats the reference angle. Thus becoming Cos(pi/3) = -1/2 since quadrant 2. Remember your Quadrants Q1,Q2,Q3,Q4 and also just remember A S T C regarding the positive values for the trig functions.
@harshbopalia
@harshbopalia 2 жыл бұрын
It is so awesome that he takes the time to explain each and every step he is doing because even I know that sometimes my brain will forget even the simplest of concepts and his elaborate steps always succeeds in making me understand the concept. 👍👍
@quicks4253
@quicks4253 Жыл бұрын
Much agreed!!! My brain is silly sometimes too LOL🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣
@madalamuthudevadas7654
@madalamuthudevadas7654 2 жыл бұрын
You are a great teacher. Your lessons are to the point. Short and sweet.
@Zapatozi
@Zapatozi 3 жыл бұрын
You got the most relaxing voice and that makes learning math a lot more easier.
@jahmaxranyeta8703
@jahmaxranyeta8703 9 ай бұрын
Thank you so much. I just had the entire topic covered in a single video.
@buttnugget9794
@buttnugget9794 Жыл бұрын
Thank you so much I have been struggling a lot with this concept but I have a greater and better understanding
@Kelly-lx8gs
@Kelly-lx8gs 3 жыл бұрын
I have a calc exam tomorrow did not take precalc for a long time so this was a great refresher, thank you!
@emmettgwilym8563
@emmettgwilym8563 2 жыл бұрын
Okay but this person explained BETTER than the one we are paying for
@nelleeeeee9628
@nelleeeeee9628 3 жыл бұрын
Thanks, I learned so much. This is very useful!
@jamesbustos1586
@jamesbustos1586 4 жыл бұрын
This mans always saving me I swear, Thanks.
@pj668
@pj668 3 жыл бұрын
Your videos are such a great help for my self studying
@christopherokine4575
@christopherokine4575 3 жыл бұрын
This is the best professor i had ever come across in KZfaq. may God give you long life and more inspiration
@daydreamsinmusic3050
@daydreamsinmusic3050 7 жыл бұрын
Your videos are the best!
@galsjgeldk6444
@galsjgeldk6444 4 жыл бұрын
This guy save so much of my physics and math test🙏🏽🙏🏽 You just saved my life dude thank you so much! Wow! All I need to knw abt trig in just 1 hr!!! This is awesome!!! Thnx sooo much!!
@lightning1759
@lightning1759 Жыл бұрын
missed a few days of class. this mans is a life saver. Really need the marks if I want to get into university
@dylan4331
@dylan4331 Жыл бұрын
Thank you , thanks for this channel ! Really benefit on learning math through this video , I would put more time in this channel become my recall back to education math . Great job !
@onenessesor9017
@onenessesor9017 5 жыл бұрын
Honestly, I've learnt more in this video than I've learned in two weeks.
@chillproductive
@chillproductive 2 жыл бұрын
this is by far the best explanation i have ever heard
@kayxmo
@kayxmo Ай бұрын
WHY DID THIS HELP ME COOK EXPONENTIALLY. THANK YOU
@yousefjabiti8863
@yousefjabiti8863 7 жыл бұрын
thanks a lot . very useful
@lolaamusu8011
@lolaamusu8011 5 жыл бұрын
This helped me so much..Thanks for uploading
@user-jw1bc3ty2h
@user-jw1bc3ty2h 6 жыл бұрын
"all students take calculus" just changed my life holy shit
@rafsansalam667
@rafsansalam667 3 жыл бұрын
"All students take cocaine" will change your life too
@truegamer5761
@truegamer5761 2 жыл бұрын
actually i prefer "All Students Take Cyanide"
@paulocesargutierrezhernand8448
@paulocesargutierrezhernand8448 4 жыл бұрын
Muchas gracias por todo tu trabajo te he seguido durante mucho tiempo.. Dios te cuide..
@viktorkira
@viktorkira Жыл бұрын
I've had a problem.. When I was studying high school, I was not really listening to the goniometry and Trigonometry, so when I went to collage, I was trying to somehow get over the Maths without this knowledge. Now I was forced to learn Trigonometry for my exam. And I have to say, without this video, I wouldn't be able to move an inch forward.. I had no experience with Goniometry and Trigonometry, and I just managed to nail It cause of you.. Thank you so much, really helped !
@pruthwirajswain7518
@pruthwirajswain7518 4 жыл бұрын
Thank you sir for your explanation by giving us very easy methods!!!!!!
@ziontech2797
@ziontech2797 2 жыл бұрын
Great Video Just helped me understand a life long confusion about radians and degrees. Keep Up the good work Org Chem Tutor👊
@yashigupta5603
@yashigupta5603 3 жыл бұрын
gawd watched all 3 vids completely and saying they r gr8 would be an understatement
@Airriii
@Airriii 4 жыл бұрын
thank you, i love all of your videos bro, please continue teaching
@awangie
@awangie 4 жыл бұрын
You're a lifesaver. Thank you.
@Phoenix-np1iu
@Phoenix-np1iu 2 ай бұрын
My class has been using the unit circle for weeks and watching this video I'm finally able to understand it
@Texashhh07
@Texashhh07 7 жыл бұрын
I wanted to say thank you so much for you dedication to helping others. This has been extremely helpful. Thanks again..
@thenokhere
@thenokhere 4 жыл бұрын
thanks man, I was really struggling here
@vishnuvundamati5228
@vishnuvundamati5228 4 жыл бұрын
Fabulously explained and taught...
@Motivation_Station_Neo
@Motivation_Station_Neo 2 жыл бұрын
Your tutorials are a lifesaver
@ComputerCurry
@ComputerCurry 2 жыл бұрын
Very thorough video, thanks!
@cesar_br5848
@cesar_br5848 3 жыл бұрын
THX BROOOOOOO I LOVE YOU! im from Brazil and your virtual classes helped me A LOT!
@cesar_br5848
@cesar_br5848 3 жыл бұрын
I prefer use the rule of "Use sempre sua cabeça", or USTC. That's a portuguese shortcut to know where is the signal from the cos sin ou tan of a given angle If the angle is from the 1st quadrant, it's always positive from the 2th, only the sin will be positive the 3th, the tangent and the 4th, the cos Of course, your way is very practical to lear if we are dealing with non exact angles (like tan of 572 degrees, which can be expressed in radians instead of degrees). To sum up It could be useful kowing how to use both of them!
@beebirb
@beebirb 13 күн бұрын
officially done with math class, but this is my favorite video in my sleep playlist. bless ✨
@hanimohamud6405
@hanimohamud6405 7 ай бұрын
Your videos are very helpful. Thank you
@nataniacello
@nataniacello 2 жыл бұрын
woaahh, this helped a lot!! Thank you so much! ❤️
@kundana2005
@kundana2005 Жыл бұрын
Thank you for this video, it's very helpful!
@GraceAjayi
@GraceAjayi 6 жыл бұрын
soooo helpful, thank god for your channel
@Dekets890
@Dekets890 5 жыл бұрын
Thank u so much so helpful my teacher could neverrr be this clear 💙💙💙💙💙
@yashsanjaykarogal9253
@yashsanjaykarogal9253 5 жыл бұрын
Excellent he has knowledge on every subject
@jasmeetkaurkukreja15
@jasmeetkaurkukreja15 2 жыл бұрын
This guy makes videos on EVERY SUBJECT. wow. What a genius
@kebedeabebe-ql5fv
@kebedeabebe-ql5fv Ай бұрын
be proude on one thing u are helping people not westing there time utubers do
@amaniyo
@amaniyo 2 жыл бұрын
I literally cannot thank u enough. Best channel best teacher thank u sooooo much.
@natelance6713
@natelance6713 6 жыл бұрын
Thank you so, so much this helped me pass my test!
@lichh64
@lichh64 4 жыл бұрын
I finally understand why we drew the tangent in that place when you started explaining the 45-45-90 triangle. Thank you soooooo much!
@FC-BS
@FC-BS Жыл бұрын
Thanks for this, it helped me to study for my test ❤
@Arijana2010
@Arijana2010 5 жыл бұрын
Incredible - thank you so much
@markkoni3499
@markkoni3499 3 жыл бұрын
U ARE TRULY THE BEST ONE EVER
@Kevessi
@Kevessi 5 жыл бұрын
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@iyketeemann 2 жыл бұрын
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@smahane5664 7 жыл бұрын
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@ethanpham7716
@ethanpham7716 2 жыл бұрын
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@johnkennethreyes2103 3 жыл бұрын
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@nice2173 18 күн бұрын
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@gr3041 3 жыл бұрын
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@shameembanu24 2 жыл бұрын
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@masonpack8019 3 жыл бұрын
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