Trigonometric Equations Single Angle 0 to 2pi Restriction 5 Examples

I should have written the restrictions as [0,2pi). I do multiple examples of solving equations with trigonometric functions in them at 1:06 4:30 9:11 12:42 15:49 This videos only includes trig functions with single angles such as sinx as opposed to sin(4x).
Please help Close Caption this lesson
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Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage / profrobbob

[@profrobbob]

A reference angle is an acute angle and it is the number of degrees between the terminal side and the x axis. The angles of 40, 220, and, 320 all have a reference angle of 40 degrees as an example.

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I'm glad my teaching style is so helpful for you. Now that you have subscribed I hope you will be able to get the help you need for your future math. Now go pass that pre-calc exam with confidence!

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Your teaching is amazing which is why I received an 82/84 on my last exam.. but the face at 9:06 is the best thing you have ever done

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CONGRATULATIONS on that 82 CJ!!! I hope you will take the time to share your success and this free study resource with your class and teacher so all current and future self-motivated students like yourself will know where to find us...BAM!!! (and I promise to always continue trying to make learning fun:)

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I would have been lost without this course. Thank you so much for sharing your love of math!

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And thank you for the sub and support and taking the time to seek outside help and choosing this channel to study with...please keep spreading the word...BAM!!!

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I have always hated trig in math and never understood anything in class but 10 minutes of your videos is like 10 hours of class you have helped me out soooooo much and right on time before exams ,THANK YOU! See you next semester keep up the good work and i love your enthusiasm . Thank you Mr.Tarrou !

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I absolutely love your energy and your cadence. Not too fast where you're skipping steps or paraphrasing, and not too slow where my mind wonders between steps. Well-explained and efficient...but I'm sure you knew that :) Thanks so much for all your videos!!

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You are so welcome Cassie Brayer and thanks for choosing my channel to learn from & no, you can never hear too many compliments! Please share my channel and your enthusiasm with everyone and remind them to like, subscribe, support the ads, share thru social media's in order to help these free educational channels groW and remain free:D

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You've just gained another subscriber! It makes my heart sing every time you say BAM because you clarified the once confusing math problems I have for homework! Thanks for taking the time making these videos helping students like me understand better and maybe even enjoy math a lot more! (:

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THANK YOU for watching, learning, subbing and "doing your homework"...that and your awesome comment, made my heart sing too Huy Dinh...especially the part about enjoying math more:) Self motivated students like you are why teachers love to teach, and why we work so hard to groW this channel...always stay motivated to learn and continue to take advantage of all the opportunities that are available these days and you will go far, your parents must be proud! Please tell your friends, classmates and teachers to watch, like, SUBSCRIBE, support the ads, share with others and help us SPREAD THE WORD :D

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That's awesome...I am honored to be a part of your future goals!

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WOW...what a compliment! My wife and I dream to be amongst the greats like Kahn and Patrick! With support from more viewers like yourself, someday we hope to make that dream a reality! So, BAM!!!...keep watching, liking and sharing my channel with others:D

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I mention this channel to my friends so frequently that I'm pretty sure I'm starting to sound like a broken record. LOVE YOUR CHANNEL! Lol. Hope your dream becomes a reality b/c I'm pretty sure that's what your videos are doing for me. =)

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We all have our own teaching style and I'm happy to hear that mine is working for you! Thank you for supporting, liking and subscribing:) Please help me grow by sharing my channel with others:D

[@profrobbob]

You're welcome, glad to hear they pick up where your prof leaves off...and THANKS for supporting by liking and subscribing!

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Seriously, thank you. I'm studying for my college precalc final, and this entire semester I've been lost. I found your videos last night, and they have explained more to me in a few hours than my prof did in the ENTIRE semester. Thank you thank you thank you. I might actually pass my final now...!

[@profrobbob]

You're welcome…and "good job" taking the time to seek out extra help and actually study:)…you make this teacher proud! Now BAM!!!…go pass that exam with your new found confidence and tell all your friends to watch and SUBSCRIBE to my channel when you do!!!

[@TheGunneyJ]

man prof Rob Bob you so awesome man, i love how specific your explanations are... alot of the times i get caught up in particular detail oriented stuff in math and Khan academy is so vague all the time... Im confident i'll do better on my pre-calc final thanks to you!

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Thank you so much for all your help! I am the type of student who has to hear things a few times for actually processing them so watching these videos after class has been wonderful. Keep up the good work!

[@profrobbob]

You are very welcome! And THANK YOU for choosing my channel to learn from and subscribe to. Stay motivated to learn, keep up those great study habits and always go forward with your future in mind:)

[@XxplatanomanxX]

thanks you sooo much unfortunately i didnt learn anything this semester because of my prof she dosent know how to explain the lesson at all to the class but because of you im finally confident to take my test n hope to get a 90 or above thank you soo much the way u explain the topic helps me alot to solve my other probllems

[@netrap11]

WOW! I had missed my class when my professor thought this. You made my life easier. that went straight to my head.

[@PrinceOfParthia74]

you know the thing is that i don't even have a book or 7π/6 a teacher.. i'm taking a precal course online so 11π/6 you are legitimately my math teacher and you do a good job of being a pro one :)

[@profrobbob]

That's awesome ***** I think that at least deserves a like and a SUBSCRIBE to my channel:) Thanks for choosing #ProfRobBob to learn from...BAM!!!

[@tsanas]

I've been looking all over for an explanation like this. Thanks.

[@olgashatunova2385]

Nice clear explanations! I recommend your videos for my students. Love your positive attitude, hand circle, bam!...One suggestions: when you show angles with hands, for students would be better to draw a unit circle and mark them. Showing Pi/6 or 7pi/6 or 11pi/6 by hand is not enough for some students. From my humble experience experience, students have to see written, drawn on a board and show angles. It stays better in their memory and helps reinforce unit circle ideas. For simple equations, I also graph in Desmos calculator the right side of the equation and the left side and students see intersections of two graphs, that are solutions and they see more solutions by doing periods. Just a suggestions to make your great lectures even more colorful and exciting! Thank you for inspiring to make my own videos.

[@profrobbob]

...by the time I started swinging my arm around in this video we had already been working on the unit circle for a long time and have included it in prior videos:)...much like you I'm sure, I also do a lot of unit circle quizzes! I will definitely try your Desmos suggestion in the future. Thanks for supporting a fellow teacher and we greatly appreciate your support of this channel! Just a reminder in case you didn't realize...the growth of these free educational channels depends on students taking the time to like, subscribe, support the ads that run and share these channels thru social medias, with other classmates and teachers as well. (example...it took us 5 years to get our silver play award for 100,000 subscribers:( ...and that was with A LOT of hard work and support from my wife answering all the comments and keeping me motivated:) Good luck with your own videos...keep inspiring in every way you can...BAM!!!

[@profrobbob]

Thanks for choosing my channel to watch and learn from!

[@rairai904]

I want to thank you Prof ! :) You help me out on the parts in trigo that my Prof can't explain it thoroughly.

[@stacy9811]

Your videos are so helpful, thank you so much! You make math so much more enjoyable and much less stressful. Can't thank you enough!

[@profrobbob]

Stacy Pitcairn you just did!Thanks for choosing, liking, subbing and learning from my channel...please keep sharing my channel and your enthusiasm with others and remind them to do the same to help these free educational channels groW and remain free!!! (supporting the ads help too:)

[@profrobbob]

I am falling asleep and will look at this thoroughly tomorrow, but you want to start by using one of your Pythagorean identities to replace sec^2 with 1+tan^2 to get your equation written in terms of one trig function (one variable...distribute the 3 and probably finish by factoring a quadratic set equal to zero. You will need to use the quadratic formula if it does not factor. Hope this helps for now:)

[@profrobbob]

Thank you for watching and subscribing. I hope you can continue to learn from my videos and turn that 90 into a 100! Good luck on your test...keep me posted on your progress:)

[@ghorticus]

Thanks for these videos, they're a great resource. My pre-calc correspondence textbook leaves a lot to be desired and your vids help me understand the finer details much better.

[@profrobbob]

+Brandon Parker you're welcome and thanks for choosing my channel to study with and please take the time to like, subscribe and share it with everyone if you continue to find it helpful:D

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@osvideosdojoao Thanks:) I have to brighten up the room every once and a while. I made this video just a couple of days ago...so now for the Holidays. Christmas for me.

[@CeeJourneyandJoy]

Thank you so much. You are a great teacher and your videos have helped tremendously in my preparations for up coming exams. I love watching your videos and your enthusiasm gives me a boost to keep sharp and stay on board. Thanks once again for all your help.

[@profrobbob]

cherica scott you're welcome and thanks for studying with #ProfRobBob!

[@ronz7684]

,, i used this video for my math flipped class ,, i really like and love the way you explained,,i used this video as intervention for my math class.. Thanks a Lot and more power..

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THANK YOU ROSE RONCADO for using my channel and I hope you continue to find it helpful...I also have a website where you might find it easier to locate topics at www.profrobbob.com

[@matthewllarena148]

,, wat

[@faithisabel25]

As always, THANKKKKKK YOUUUU for posting these helpful videos. You're such a great teacher!

[@profrobbob]

...and your such a great student!!! Wish I had a classroom full of studiers like you...BAM!!!

[@profrobbob]

OMGoodness...what an AWESOME comment!!! You just don't know how much my wife and I appreciate the support from subscribers like you:) If all our viewers were sharing like you, we would have that "M" next to our subscriber count in no time!!!...lol I hope your friends never get tired of hearing how passionate you are about learning=)

[@georgesadler7830]

Professor RobBob, thank you for another tremendous video/lecture on Solving Trigonometric Equations Single Angle zero to 2 pi Restrictions. These examples take practice and patience and a good understanding of the Unit Circle. Your interval includes 2 PI, which is an error, it should not include 2PI.

[@Ksenia584]

I like the way the chalk made cloud when your clap your hands and said "BAM!" It's like you're a math magician. Haha.

[@profrobbob]

acatnamedshoe LOL Thanks for watching, learning and subbing too:)

[@tunguyen6314]

This video helped me out so much. Thanks a lot I love all your videos that I've seen so far.

[@profrobbob]

BAM!!! You're welcome Tu Nguyen and thanks for watching, learning and subbing! "SPREAD THE WORD" :D

[@Flaggot0308]

Thank you so much! You're a great teacher because you explain each step very well and you keep it pretty exciting (some math teachers can be very monotoned) I'll definitely be using your videos to help me study for upcoming tests!

[@DrAnimePhD]

You're like the Bob Ross of math.

[@profrobbob]

+DrScaphandre thanks...I don't paint but did recognize his face when I look his name up:)

[@meischoice]

Hey, you posted this video on my Birthday (last year) What a very nice Birthday Present :D

[@susan4jc]

First example at 3:35 solutions for sinx=0 is 0,pi,and 2pi?

[@luvdatkawaii]

Sir, I adore how festive you are! Although this video is nearing its 5th year anniversary, Happy Holidays to you and your family!(:

[@profrobbob]

THANKS...lol, I just wore that shirt yesterday! Good thing about holiday shirts...they never wear out...BAM!!!

[@profrobbob]

Happy holidays to you as well:D

[@rave10]

You are helping me get one step closer to becoming an engineer.

[@anjalirana860]

On 13:52 how did you get sin2x=2sinxcosx?

[@tosasaurus5783]

I need some more BAM! in math, good thinking

[@profrobbob]

There is plenty of BAM!!! in my almost 600 videos:)

[@profrobbob]

That is what you get from your calculator when inverse is limited to act as a function, but sin(7pi/6) is also -1/2 and sin(11pi/6) is -1/2 too:)

[@theresanoelle]

at 10:34 why does 1-sin^2theta-sin^2theta+sintheta=0 become -2sin^2theta+sin^2theta+1=0? are you multiplying everything by -1?

[@theresanoelle]

nevermind i just figured it out xD

[@profrobbob]

Theresa Harris good job on not giving up till you "got it" ! Thanks for watching and learning from Tarrou's Chalk Talk...please Like, SUBSCRIBE and share with others too:D

[@naj301]

Great video, just a quick question. What is the name of the rule that you used to multiply the first term by the constant 6:08 ?

[@profrobbob]

+TheJet 1 I don't know the rule's name, it is just a technique to factoring quadratics. I cover it in this lesson, kzbin.info/www/bejne/bqWQpoWvi9Skla8

[@naj301]

Thank you!

[@profrobbob]

+TheJet 1 :)

[@Grace-eh2de]

THANK YOU. You are my ticket to success in trig. Thanks to your vids I made a 100 on my last test. :D !

[@profrobbob]

BAM!!! I see you are still watching more videos Grace ...no wonder you got that 100%...CONGRATULATIONS! Please share your ticket for the #ProfRobBob show with EVERYONE! Tell them to like, SUBSCRIBE, support the ads, Support the channel and spread the word thru social media too...help this free educational channel groW and help others! Help us get 100,000 subscribers by 2015

[@IntensePeppers]

I'm confused. I just watched your inverse trig functions video and you explained how inverse functions are restricted. i.e sin^-1 is restricted from -pi/2 to pi/2. But here in the first example one of the answers was pi, which is outside that restriction. What's the deal?

[@chordsequencer001]

Right, right for sin(theta) = 0, 0 is a particular solution, k(pi) is what is known as a "general solution" for sin(theta) = 0, where k is in Z. When tackling theta by itself, we can only obtain the "particular solution". But in general, its arcsin(0) + k(pi) where k is in Z.

[@ronz7684]

this will help --- my class,, continue your works ,,i used it in math flipped class online intervention for a thorough understanding my math class .... God bless..and Thanks a Lot !!!

[@khizarirshad2331]

what do you say when you jump in the beginning?

[@profrobbob]

BAM!!! Khizar Irshad if you keep watching and learning from my videos I've been told you might even start saying it yourself:D Thanks for watching and subbing...SPREAD THE WORD too!

[@hermanwang7978]

These videos are great! Keep updating!

[@profrobbob]

+Herman Wang thanks for studying and subbing to my channel!...and please keep sharing:D

[@393blueangel]

i'm confused as to what reference angle you're talking about... help please!

[@profrobbob]

What's that...another engineer in our future?!...Congrats and good luck! Thanks...but no presidential future for this teacher, I'm happy just teaching math to the world...but feel free to start a campaign to make "Tarrou's Chalk Talk" a KZbin favorite!

[@michellejohnsph.d.6098]

I like your style of teaching. I recalled factoring better when you did no use the grouping method. Thanks

[@profrobbob]

Thank you for watching and your support.

[@profrobbob]

@tsanas Your welcome. Glad you found me:)

[@ayovalerie1995]

I have a question PLEEEEASE RESPOND I HAVE FINALS NEXT THURSDAY! So at minutes 16:20 when he uses the Double Angle identity 2cos^2x-1 in replacement of cos2x..... how do I know to use THIS specific identity? FOR EXAMPLE: in my textbook cos2x there are three different identities for it: cos2x = cos^2x-sin^2x = 2cos^2x - 1 = 1 - 2sin^2 How would I have known its supposed to be the second one?

[@profrobbob]

Knowing you are going to solve an equation, it is best to keep everything in terms of one variable... or trig function. That is why I used the second identity. I hope you did great on your exam. Sorry for the late reply.

[@ayovalerie1995]

It's actually tomorrow! BUT THANK YOU! Currently watching all your videos haha

[@nikejustdoitish]

Which trig identity did you use at 13:40 ?

[@philipwest2551]

As a teacher I frequently recommend your videos to my students as a was to reinforce the ideas we have discussed in AP Calculus. However I must raise a point of concern in this video. The inverse sine of a trig function gives only one answer - for you to write arcsin(-1/2) having two solutions is surely incorrect - try using your calculator! It would be better perhaps to explain that there are two possible answers to the equation in the given domain and maybe avoid using arcsine. I suppose this is similar to x^2 = 4 and x = sqrt(4) being different equations. I love your videos and hope you don't mind my input :)

[@profrobbob]

It would have been good for me to remind the viewers, the students, that I am solving the question for the domain of [0,2pi) as indicated on the chalk board which is why there are two solutions. You are of course correct that if we are using arcsine as a function there is only one answer of -pi/6 which is neither 7pi/6 or 11pi/6. An old book I used to teach out of would use lower and upper case letters on the inverses to differentiate between inverse relations and functions. I can certainly stop using this notation in class:) Unfortunately I can no longer add annotation corrections thanks to KZbin's changes. I hope I did not confuse any of your students! Thanks for using my videos as a reference for your students.

[@lukundoabigail2546]

Wow thankyou You're the best🙌

[@profrobbob]

Thanks for watching!

[@morgan5169]

Can I have a teacher trade off please. Rarely do I see a math teacher get passionate about math, your students must love you

[@profrobbob]

+Morgan Huyler thanks for the kind words and for studying and subbing to my channel! Sounds like the next best thing would be to share my channel with all your friends, you can all watch videos and do your homework together...BAM!!!

[@jennijones4369]

How do you find the exact value for a problem such as tan(arccos3/4) .... ? Seeing how 3/4 is not a measure on the unit circle... and the (tan) sitting in front causes extra confusion for me.

[@profrobbob]

It would be great if you watched the entire lesson, or you could start watching at 12:18 :)

[@jennijones4369]

Thank you so, so much!

[@profrobbob]

Jenni Jones thanks for putting the time into your education:)

[@jocelync8236]

Why do you need to use the inverse??

[@sbk1398]

Thank you very much for this. Can u do one that has tangent in it? Where you have to figure out where it's undefined? That'd be very helpful.

[@profrobbob]

I have a video on graphing Tangent. kzbin.info/www/bejne/oX6zpaWdd7Rqg6c One way to identify where tangent is undefined is to graph it, find one vertical asymptote, and then the values where tangent is undefined will occur every distance of the period. I hope this is good enough to be of some help. I am currently trying to Close Caption my videos.

[@sbk1398]

ProfRobBob Thank you. This is fine.

[@YAHOOOOOO5]

you're better than my professor lol

[@profrobbob]

+YAHOO thanks for watching, learning, liking and subbing!

[@sammygarcia908]

Thank you sooo much!:) I have finals next week!

[@alancruz2556]

Hi ProRobBob Your videos are very helpful, so thank you! I was wondering why the title says single angle when you're solving multiple-angle equations? Just Asking

[@sarahgray3371]

You are my math savior

[@profrobbob]

+Sarah Gray thanks for choosing, liking, learning and subbing!

[@TteamEdwarD16]

thank u so much for being an awesome teacher!!!

[@profrobbob]

marwa_ 5566 you're welcome and thanks for watching, learning and subbing...please spread the word:D

[@defeatedwyvern]

I have a question sir. In the first example, isn't the restriction supposed to include 2pi? why wasn't it included in the solution for sintheta=0? Thanks :))

[@MeicoRaider]

I love your handwriting.

[@profrobbob]

THANKS:)

[@profrobbob]

Well obviously it is one of the double angle identities...but...to prove it is true. Write sin2x as sin(x+x) and use the sum identity for sin and you get sinxcosx+sinxcosx which is equal to 2sinxcosx:) Now this is assuming you accept that sin(a+b)=sin(a)cos(b)+sin(b)cos(a) which requires another proof!

[@DessertUnicorn]

u r a better precal teacher than mine...

[@profrobbob]

Thanks for studying and subbing...sounds like the perfect time to share my channel as an "after class study reference" with your teacher too:)

[@jessemeng8249]

I've watched all your trig videos till now. But I still don't get is there a difference between writing func theta and func x? func can be any trig function. This is because sometimes I see you using x as a variable and sometimes you use theta, beta exc exc.

[@profrobbob]

There really is no difference. Most of the time my trig, precalc, calc books etc will use Greek letter for variables that represent an unknown angle.

[@profrobbob]

Looks like you will be having another birthday in a couple months then! Let me say "Happy Birthday" early :)) (If you were my student I would have written HB on the board)...anyway, glad you liked your present..hahahahaha. Keep watching and supporting my channel...I grow through your support. Thanks!

[@xSazakura]

you're my savior!!!

[@profrobbob]

Double angle identity for sin.

[@NikeBOY9769]

you teach better than my math teacher

[@YAHOOOOOO5]

i used quadratic in the second problem, same answer :)) Thanks

[@scrollsiddur5348]

In the first example, why can't you just factor the left side to 2(sinx)(sinx - 1) and then divide both sides by 2? Then you get sinx = 0 and sinx = 1

[@profrobbob]

+Scroll Siddur Both of the terms on the left hand side do not have a common factor of 2. That is why you cannot factor out a 2 from both terms.

[@rue3366]

doesn't sine^-1 (0) also equal 2pi?

[@profrobbob]

sine^-1 (0) has an infinite number of solutions but only 2 of them are within the restricted range 0 and pi. The answer to your question is yes, but 2pi is not within the restrictions to allow inverse sine to act as a function.

[@theanimeregimen2078]

Most complicated factoring I have ever seen at 7:30. I simply use the simple FOIL method 2sin^2(x) - sin(x) -1 to:(2sin(x) + 1) (sin(x) -1). Learning the Foiling methods can save multiple steps from the grouping process.

[@profrobbob]

+TheAnimeRegimen +TheAnimeRegimen As you leading coefficient and constant gain factors and are no longer prime numbers the FOIL method...aka trial and error...is going to become very frustrating and time consuming. That is why I am showing a process to factor these quadratic trinomials. This was just a simple example.

[@theanimeregimen2078]

+ProfRobBob Ah, gotcha. Haven't had to deal with any problems of that magintude yet. Guess I will have to learn this method sooner or later.

[@profrobbob]

+TheAnimeRegimen You don't have to learn this method. When I was in high school we were only taught the FOIL method, or what I call trial and error. I saw this method for the first time when I was tutoring someone in Algebra in their book and was pissed I was never taught this technique of factoring. That trial and error can be really frustrating at times! Thanks for watching too:)

[@theanimeregimen2078]

+ProfRobBob No Problem! Loved the video where you slammed your chalk against the board. The enthusiasm is real! hahaha

[@profrobbob]

+TheAnimeRegimen always keep learning and thanks for subbing too...BAM!!!

[@gennaclement7047]

super helpful!!!!! thank you!

[@profrobbob]

BAM!!!

[@orangething7344]

Jesus I love your hand writing...

[@profrobbob]

Thanks for watching!

[@matiasgipler4724]

9:06

[@profrobbob]

Matias Gipler :) ...cheesy and helpful at the same time...BAM!!!

[@n.fer.2596]

god I hate math. like a lot. but you make it pretty easy!! wonderful job! Mayb ill pass that quiz tomorrow:) Also you are wonderfully weird. I mean like in the best way. Great energy!

[@themasterbather]

I love math so much.

[@profrobbob]

BAM!!! That's something I don't hear often...thanks for liking and learning...please be sure to sub and share too!

[@brennano4509]

erasing skill level:100000000000000000000000000000000000000000

[@profrobbob]

I'd say "that's some gi-normous skill level"...lol Thanks for noticing Brennan:)

[@profrobbob]

@ronaldhino090 Thanks

[@marcv2902]

it would be entirely easier to do a U sub and just use quadratic formula. or at least it would look a bit less confusing. Factor by grouping is just outdated and tedious imo but thanks for the video

[@rcanterella1126]

cant for somereason understand where you got 7pi/6 and 11pi/6 youre awesome btw

[@profrobbob]

Thank you for your kind words. It sounds like you need a review of the unit circle kzbin.info/www/bejne/hICXeWePh7SXp80 or how inverse trig functions work kzbin.info/www/bejne/nqnNnqd6jb12sLc Those are the two angles where sine is equal to -1/2

[@juanfigueroa1704]

Very helpful !

[@profrobbob]

+Juan figueroa thanks!

[@vladusa]

I watch Tarrou like I watch Netflix.

[@profrobbob]

I hope that's A LOT!!! ..and if it is, please share this channel with EVERYONE and remind them to like, sub and keep sharing so we keep growing...BAM!!!

[@rainsie3438]

Thank you ! :)

[@Smiirffable]

got it. Thanks

[@profrobbob]

You're welcome Erfan Maleki glad you "got it"! Thanks for learning and liking but please don't forget to SUBSCRIBE, Support and share with others to help my channel groW :D

[@Smiirffable]

ProfRobBob Done done and done. thanks again.

[@profrobbob]

Erfan Maleki Woooo...Hoooo!!! THANKS for being so prompt too:)

[@lamyasms4656]

I fail to understand why sine2theta = 2sine theta cosine theta

[@profrobbob]

This page of proofs should help, www.themathpage.com/atrig/double-proof.htm

[@profrobbob]

Now the proof of the sum and difference identities is a bit more complicated, pages.pacificcoast.net/~cazelais/173/idns-proof.pdf

[@lamyasms4656]

it is indeed, Cant thank you enough for the help and for the amazing video. keep up the good work :)

[@lamyasms4656]

massive thanks for the close captioning. its really making stuff easier and is helping me understand smoothly:)

[@profrobbob]

Really glad to hear it's helping! I had alot of request but not alot of help:( If you know anyone or any company that would help us finish up these last 150 or so videos for FREE I could get back to making lessons again. I've pretty much spent the last year and a half closed captioning!

[@acab247]

Same here! Tarrou for president!

[@michellec.4291]

The factoring part is kinda confusing :/

[@profrobbob]

Here are all of my factoring videos in one playlist for a refresher, kzbin.info/aero/PLGbL7EvScmU7ix7CX3niSxTntHtxjlwU5

[@bendillon7497]

Ok I'm not following. Why is 2sinx equivalent to 2sinxcosx

[@profrobbob]

2sinx is not the same as sin2x...or sin(2x) which can be rewritten into 2sinxcosx. I used a Double Angle Identity.

[@collinh24]

U substitution is much easier in my opinion

[@iananderson4929]

how r ur knees doing after all the intros to these videos? you ever think about just making one intro for all ur videos?

[@profrobbob]

lol...my knees are good:) A common intro would take all the fun out of it...and occasionally I do switch it up a bit!

[@iananderson4929]

i was totally kidding but good to hear. i passed trig today. thanks bruh.

[@profrobbob]

BAM!!! and congrats! Guess watching all those intros paid off:)

[@Takingprofits]

I fucking love you