Sum and Difference Trigonometric Identities

[@Slaynn44]

You are a lifesaver. I am a 34 year old married soldier with three kids going for a computer science degree. Due to time and availability I am doing everything online. Math through an online program is extremely painful. Your videos turn my livingroom into a classroom with a high level of motivating energy. BAM! I'm doing my homework!!

[@daniberg121]

How'd it work out for you? I'm in the exact same position as you now, minus the soldier part. Feeling a bit old for this field but pushing forward, nonetheless. If anything, I'm glad I ran into your comment.

[@Slaynn44]

@@daniberg121 it worked out decently well. I landed a job at a large consulting company making enough money to comfortably travel the world while working from home. It's worth it.

[@ThatTechnologyNerd]

I just want to thank you on behalf of every student in the world that is having problems in math. Your videos are by far good enough to make your viewers pay to watch them and I greatly appreciate that you keep your videos free. You can tell that you truly love your job and you are the reason myself and 1,000,000 other kids have better grades in math.

[@profrobbob]

THANK YOU ThatTechnologyNerd for taking the time to acknowledge all the things we strive for on this channel and taking the time to "thank the teacher"! Self motivated students like you are the exact reason that we continue to work hard to groW this channel by simply asking students to like, subscribe, support the ads, share thru social media, with their friends, classmates AND teachers...at the same time reminding those new viewers to do the same. If everyone did that, we would have a million subscribers by now and students wouldn't have to work so hard to find my channel...BAM!!! Thanks again...we truly appreciate your support and awesome comment:)

[@KiwiBloodstain]

I have failed my last three trig tests because my college professor can't explain anything worth crap. She goes through 3 sections in one day and takes no questions. I have learned so much more watching this 15 minute video than I have in over 3 months of class. You will save my trig grade! :D THANK YOU SO MUCH!!!!!!!!!

[@mikemo90]

God, I love this guy. I've been struggling in my college Trig now for 2 months and I haven't been able to understand any thing. I found this guy yesterday and everything has just started clicking in my head. Mr. Tarrou I thank you for being an amazing person, please keep it up there are numerous people like me that you have and will help by doing this channel. BAM! Go do your homework!

[@ojanyramos2244]

I'm in college taking PreCalc and these videos are WAY more helpful than the lecture my professors provide, great work!

[@profrobbob]

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[@kilogreene8738]

You know when I turn in my tests I jump at my professor and go "BAM! Give me an A!" 60% of the time it works every time. But for real your videos have always helped with really understanding what it is I'm doing. Thanks a million!

[@profrobbob]

Thanks for watching and taking the time to thank the teacher...BAM!!! Sounds like a perfect time to share this free resource with your teacher too:D

[@profrobbob]

CONGRATS!!! Now thats the kind of percent a KZbin teacher likes to hear...the 92% that is:) And now that you know where I am I hope you will be back...and share my channel with your other classmates!

[@Ninag13]

The broken light, great comedic relief! Thank you so much for posting your teachings. I greatly appreciate them! Gives me a much better understanding of the subject. You make Trig easy and fun! ;) Can't get enough of your videos!

[@jamilinam17]

Honestly, I have been watching your videos for the past 2 hours and literally, the concepts that i never understood for weeks, are now on the tip of my fingers! Ur just an amazing person! Thank you so much!

[@profrobbob]

You are so welcome Inam Jamil and thanks for taking the time to look for additional help and chose my channel to subscribe and learn from...and took the time to share your learning experience with us! Please share with your friends, class and teachers too:D

[@joeboei]

I just watched a man fix chalk board light bulbs

[@profrobbob]

BAM!!!

[@MathTeacherMusician]

I'm giving my students a break and getting (forcing, suggesting:)) that they watch you. We all get a great kick out of them and they work great. After teaching the "easy" math for many years i now have the opportunity to teach a higher level and your videos have helped more than you can imagine. Thanks:)

[@profrobbob]

THANKS Joe!!! It's always nice to hear that a fellow teacher is sharing and supporting! My wife and I have put alot of time and effort into the growth of this channel, mainly just trying to spread the word (since we've never seen a math video go viral:) and so everyone who wants to study has the opportunity to do it for free! Please share with fellow teachers and congrats on the new classes. Seems I'm moving in reverse...I'll have 5 preps next year, including 2 classes that are not honors or AP...seems there are just not enough students to fill those classes:(

[@EP-rq3pn]

This was such a great video, very clearly explained, thank you! I love how you re-drew the bottom light bulb to look broken after you broke it.

[@profrobbob]

THANK YOU for watching, subbing and paying such close attention to detail..you should continue to do well in math!!! Please tell your class and teacher to watch and do the same...BAM!!!

[@jinsu.c]

im a sophomore in high school and my teacher is terrible at teaching. These vids really help me understand everything thats going on. thank you

[@profrobbob]

You're welcome ***** Thanks for watching and please share my channel with your class and your teacher as an additional study reference for the students and please remind everyone how important it is to like, SUBSCRIBE and share these free educational channels to help them groW and remain FREE :D

[@anthonyh4476]

BEST MATH VIDEOS I'VE SEEN! You have helped me so much in my pre-calc class. My professor is not even as close as good as you are at explaining these topics. LOVE IT!

[@profrobbob]

+Anthony H THANKS for the compliment and for watching! Please take the time to like, sub, support the ads and share this free educational channel with your friends and classmates too:D

[@ShamelessHorse]

I have been mucking around with sin and cos drawing circles in computer programming for years without really knowing what I was doing, so this x and y based style makes much more sense to me than talking about opposite, adjacent and hypotenuse sides.

[@profrobbob]

Glad I was able to wash away that muck ShamelessHorse ...gotta stay out of those stalls without boots on:)...lol

[@ayran.4498]

You don't know how much time I spent on google just to find the exact equation on my worksheet! Thank you very much! Subscribed😊

[@profrobbob]

Thanks for studying and subbing...please share this free resource with your teachers too:D

[@profrobbob]

I have that correction in the description of the video and there is an annotation correction. Either you settings are set to not show annotations, don't have Flash, or watching on an iPad maybe. Sorry for the error. Thank you for watching and the time stamp is nice for questions:)

[@profrobbob]

What is that text that can be instantly translated into almost any language you like? Why yes, those are KZbin Closed Captions.

[@isaacmarquez7777777]

+ProfRobBob did you hear the one about the guy that got his whole left side cut off... well hes all RIGHT now! XD

[@codecat8430]

Kind of like the guy who fell into the upholstery machine, he's all re-covered now. :-P

[@yasuu2342]

i see this guys videos, make sense and ok they are easy. I take the test at school and I don't remember shit

[@BennettCHS]

Great video and great channel. I will make sure to recommend you to others. I thought I wasn't going to survive in PreCalc 2 with my 75 year old teacher who is tough to understand. THANK YOU SO MUCH

[@dolfglenardresuello7416]

the answer in your 1st example is sqt. 2 - sqt. 6 over 4

[@RedNuii]

+Dolf Glenard Resuello he corrected himself using annotations. Turn them on and see for yourself

[@profrobbob]

+RedNuii thanks for the help by pointing that out!

[@anyannie6100]

that's what i was thinking!!!

[@drmoha1]

yh it confused me heheh

[@Ashley-qe5by]

Whew okay I’m glad someone mentioned that, I thought I forgot had to multiply fractions for a second 😅

[@tastythaitreat]

You are absolutely amazing. I really do appreciate a teacher with so many charisma. And I see how you always write your viewers back. Anyone can clearly see that you have a passion for teaching others and it is one that I can really appreciate. Thank you for all your videos they're amazing!

[@profrobbob]

THANKS for watching and noticing all the little details Linda Thai ! My wife helps a lot with comments and teaching is defiantly my passion...don't forget to like, subscribe and share to help these free educational channels groW and remain free:D

[@Lasthope4269]

Man why cant all math teachers be like you? XD Mine for the past 2 years have been foreign and they talk fast and i feel like they're speaking another language. I was hoping i could seek help on youtube. Then i found Mr. Tarrou. You explain a lot in so little time. Its amazing! You are my go to math teacher now. :) Thank you.

[@condor3902]

My college pre calc teacher doesn't teach very well. These videos have helped me through trig SO MUCH. I can't thank you enough. Thank you :D

[@profrobbob]

You're welcome Connor Loch and THANK YOU for taking the time to find help on KZbin and chose my channel to learn from and subscribe to! Sounds like you should share my channel with your teacher and class as an additional study reference for tutor help after classroom hours! WIN, WIN, you're a hero and I get more subscribers and continue to groW and help others...BAM!!!

[@aymeeteee]

I always come to you when I have no idea what I learned in trigonometry (which is all the time) and its really helpful!

[@profrobbob]

Thanks Amy...please take the time to subscribe and share this channel with your class and teacher as a study reference for other self-motivated students like you:D

[@ThatRandomBlackGuy]

xD that intro scared the heck outta me

[@profrobbob]

get ready...there is much more to come!!!

[@ThatRandomBlackGuy]

ProfRobBob thank you by the way, it really helped out alot :D

[@profrobbob]

you're welcome...thanks for watching and please help us keep growing by subbing and sharing this free channel with your classmates and teachers:D

[@ThatRandomBlackGuy]

ProfRobBob i'd be happy to!

[@Ahmed-qc3bh]

Cause u r a pussy nigga

[@profrobbob]

Thank you for the kind words...it's students like you that make me love my job! Speaking of that; I loved your "jump on it" video and commented that I need to do a cameo appearance the next time you do a high school production...you keep up the great job too!

[@profrobbob]

You're welcome...and THANK YOU for supporting and subscribing:) One of my goals with these videos is to "Make Math FUN" while learning, one student at a time...and it looks to me by your comment that I have converted another one! Please help me grow by sharing my channel with your friends:D...I appreciate all the support.

[@RadicaLxIce]

This vid definitely helped me out a bit.. these kinds of problems are the ones my teacher gave at the start of class, except we had to do them in 2 minutes, not 14. And then she just pushed right forward to way more complex and ANNOYING expressions. Then she usually goes on to say "remember there's room in my non-honors precalc class for those of you taking this long." Like cmon. Anyways, thanks for the video, helped me keep up today.

[@profrobbob]

You're welcome, Glad I could help...please help us by liking, subbing and sharing with your teacher so ALL current and future students know where to find free study help after class...BAM!!!

[@sassonaredab3882]

Mr. Turoo, you're like, the guardian angel of math.

[@profrobbob]

Thanks for your efforts. I will look up both colleges and send my letter to whatever they call their student/academic learning center. I appreciate the support!

[@profrobbob]

Thank you for that endorsement. That is quite a compliment considering how much math help is available on youtube! Please help me grow by sharing my channel with others who may benefit:D...thanks for your support.

[@profrobbob]

I didn't just work on the top portion (numerator), I applied the sum identity for tangent to rewrite the expression. Thank you:)

[@georgesadler7830]

Professor RobBob, thank you for a mammoth video/lecture on Sum and Difference Trigonometric Identities in old fashion everyday Trigonometry.

[@profrobbob]

More than one comment and video watched....you are working hard aren't you?!...speaking as a teacher, great job on the extra effort and thanks for watching and supporting:)

[@profrobbob]

Oops...there is a little mistake there:). 2*2=4 and not 2! Thank you so much for watching and keeping me straight.

[@marissaroland]

We have a song that we sing to remember what to do in regard to sin and cos! Thank you so much for you videos. You are a savior.

[@profrobbob]

Well I'm glad to see that you decided to seek help on KZbin or you never would have found my channel! I'm glad you find my teaching style so helpful and choosing me as your go-to teacher! I'm looking forward to having you as one of my KZbin students. Just a thought...If others in your class are struggling too, maybe you could start a study group using my videos...it helps when you have others to bounce questions around with:)...and please share my channel with your friends too:D

[@profrobbob]

That's a true statement. But to get an exact answer we need to use angles that are on the unit circle and 15 degrees is not. Thanks for watching:)

[@romariodixon7587]

I'm new to your channel and for real, you make each topic so clear to me. Coming from a C, I got my first A on a Chapter Exam because of your videos

[@profrobbob]

CONGRATS Romario...that's certainly something to be proud of! If you continue to find this channel helpful please share it and your success with your teacher so ALL current and future students, who are self-motivated like you to study, can have the same opportunity...BAM!!!

[@profrobbob]

All of my Trig proof videos are in my Trigonometry playlist. They are videos numbered 22 to 30. I am not sure of what you are asking about. I know I did not do any videos on power reduction.

[@slavrinc4281]

I think it's hilarious that he said 'you dont wanna be drawing little triangles everywhere,' cause I totally do. Great presentation, really helped fill in the gaps of my textbook, thanks!

[@profrobbob]

You're welcome...thanks for studying with us! Don't forget to sub and share this free resource with everyone...BAM!!!

[@firippumartinezu1782]

I'm studying for my final and this was a very quick and thorough explanation. Thanks for the video. You seem like an amazing teacher.

[@profrobbob]

You're welcome...thanks for studying and subbing..I hope you pass that final ;like BAM!!! and after you do, please share this channel with your teacher and classmates too:D

[@profrobbob]

Thanks for understanding and the complimentary comment...and please continue to watch and share:D

[@nocontrol0]

Your first problem, sin(195), resolves -0.5176380902050415246977976752481 on the calculator, however, your answer of (sqrt(2) - sqrt(6)) /2 resolves -0.5176380902050415246977976752481. Your denominator should be 4 and your result would be the same as the calculator. I'm sure it was an unintended blunder. I should tell you I am glad for your time and efforts. I encourage you to continue these lessons; many high school kids are appreciative. Thank you again.

[@profrobbob]

There is an annotation correction and I have a note about this in the video description. Sorry about that:)

[@profrobbob]

I wish annotation corrections were not Flash so they would show up on iPads and computers without flash. I corrected this problem...because 2*2 does equal 4 and not 2!!! Thanks for the note. I am going to add the correction do the description of the video as well:).

[@profrobbob]

I hope you are feeling better. Sorry I missed your comment. Thank you very much for the support again.

[@profrobbob]

Yipppeeeee...another believer..."making math fun" one subscriber at a time!!! Thank you for the nice comment and support by subscribing:) Please share with others, cause that's how I grow:D

[@profrobbob]

If Sin A = 5/13, your reference triangle could be set up with y=5 and r=13 giving you an x=12 with the pythagorean theorem. With Tan let y = -sqrt(3) and x = 1

[@profrobbob]

Thank you for watching:) I am thrilled I could help.

[@billytu5695]

Thanks! My teacher rushes through this stuff so I don't understand it. Have a thumbs up from me.

[@profrobbob]

THANKS...please take the time to like, SUBSCRIBE and share this free channel with your teacher, in case the rest of the students are having the same problem!

[@billytu5695]

i already liked it

[@profrobbob]

Congrats Nick...dual enrollment is a bit harder but the rewards are much greater in the end! Just keep up those good study habits and you will do great! (after all, you have my videos to fall back on next year:)...lol

[@MisunderstoodAlpaca]

I like the chalk board. It's very old-school.

[@profrobbob]

THANKS..I too LOVE my chalkboards! And this one is from an old school built in 1926...I'm one of the only rooms at the school I teach that still has slate chalkboards in my room...the other ones have all been replaced with whiteboards:(...It's so sad Thanks for watching too!

[@profrobbob]

First of all, thank you for such a heartfelt comment, they are the ones that make all the hours worthwhile! I as well hope I can continue to help you through your classes. If you go to the "HOME PAGE" of my channel you will find "playlists" for the classes that I have videos for so far. If you watch my intro video it should help give you direction on how to find individual subjects....hope this helps:)...and if you like my channel be sure to share with your friends:D Thanks

[@profrobbob]

THANK YOU!!! I added an annotation correction for now and will repost this in the next couple of days with a correction that people with iPads, iPhones, etc will be able to see. Thanks for watching and letting me know again about my small error. I great appreciate it.

[@profrobbob]

THANK YOU for the compliment and for seeking out extra help. I'm glad that my teaching style is so beneficial to you and I hope you will make me your go-to KZbin teacher throughout the rest of your math studies:) Be sure to spread the word about my channel to your classmates too:D

[@profrobbob]

You're welcome so much! And THANK YOU for supporting by subscribing and recommending my channel to others. Positive comments and viewers like you are what helps my channel groW!

[@profrobbob]

And THANK YOU for watching and subscribing...I hope you go in and pass that teat like BAM!!!

[@briannacorrine3051]

Wish I had you as a teacher! You've helped me a ton and your blackboard is awesome!

[@profrobbob]

Thanks for watching and subbing...at least I can be your KZbin teacher!...and if you share my channel with your teacher the rest of the school can too...BAM!!! I love my blackboards too, thanks again!

[@rishiklad1876]

this is amazing... you were able to help bring clarity to a subject that even my math tutor failed to teach me. thanks so much mr. tarrou!

[@profrobbob]

You're welcome...I hope that earns me a like and a new subscriber too:) ...and while you're at it...please keep sharing so we keep growing:D

[@MissCaptainEpic]

You are a life saver. Hopefully I do well on my unit test coming up soon. Plus, you're really energetic and lively, and I kind of zone out on other monotonous KZbin videos!

[@profrobbob]

I too hope you pass that unit test like BAM!!! jessebun ! Thanks for choosing my channel to watch, like, learn and sub to...please tell all your friends, class and teachers to watch and do the same to help us groW, thanks:D

[@profrobbob]

We teachers all have our own style...mine just happens to be a bit on the entertaining side. My mission in life is to "MAKE MATH FUN" while learning....keep watching and sharing my channel...thanks:))

[@profrobbob]

Thanks for understanding and I hope you will continue to choose my channel or share it with others:D

[@profrobbob]

That's the first time I've gotten that as a title...but my wife and I really like it! She says we should put that on a t-shirt:) Keep watching my videos...maybe you'll see it someday and say to yourself "I gave him that name"..thanks again for the nice comment.

[@profrobbob]

If you want to share where you go to school I would love to start by sending them the introduction letter and information I have put together...otherwise thank you for the direction, there are so many departments listed on each college website that it's a little overwhelming where to start. Being a student on campus yourself can be a huge advantage in my quest to spread the word. Thanks a gain:D

[@MrCraig2812]

You're Awesome Man... Really helping me with my online Maths course... I review everything with your videos to make sure I haven't missed anything :) Keep it up bro!

[@profrobbob]

+Craig Farrell glad to hear that you are finding this channel so helpful and thanks for taking the time to share your learning experience with us! Thanks for liking and subbing too...please tell all your friends and classmates to watch and do the same to help this channel keep growing:D

[@gouravpardhan6219]

Nice video sir it really help me I am from India🇮🇳

[@profrobbob]

Thank you from Florida for watching Rajesh! Glad I could help. I hope you will share this channel with everyone and please remind them all to like, subscribe and keep spreading the word to help this channel keep growing and helping others for free:D

[@PrivateAmericanAcademy]

@ProfRobBob You are the real MVP!!! Thank you so very much! You made my semester so much easier!

[@profrobbob]

+Jaiye Owolabi you are very welcome...thanks for choosing my channel to study with and sub to and for taking the time to study in order to make that semester easier...BAM!!!

[@profrobbob]

Do you mean the annotation I had to add? Because 2 times 2 is 4.

[@maheshvra5995]

I'm watching your videos for advance studying and sir, you never failed to amaze me. Thankyou so much! Keep it up! BAM!!

[@profrobbob]

Andrew Villaruel you are so welcome and THANK YOU for choosing my channel to learn from and subscribe to!

[@maheshvra5995]

Aye sir!!! :D

[@profrobbob]

Andrew Villaruel :)

[@lukehiebert9944]

Absolutely the best Math help on KZbin!!!!! Thanks so much, Please Keep it up!!! :)

[@profrobbob]

+alfridokiller1 The answer to your question is no for the very reason your answers have the wrong sign. Do tan (135+30)

[@profrobbob]

Thanks...I'm working on just that right now. I will be teaching AP Calc next year and I'm currently working on that library.  Thanks for supporting by subscribing and I look forward to another photo from that best dressed dog:)

[@profrobbob]

Thank you for the enthusiastic comment. So glad I could help! Could I ask a favor in return?...If I wanted to spread the word to other students such as yourself, at your school, what department would I want to contact?...Math Department? Student Center? Academic Dean?...any suggestions would be greatly appreciated!

[@danhassan2108]

My quick calculus included this in the review, just wanted some fast standard examples of them, Thank you bro.

[@profrobbob]

jewish scientist you're welcome!

[@profrobbob]

It helps to love it when you're teaching it! Keep watching...maybe you will learn to at least enjoy it more:)

[@profrobbob]

Just follow the signs of the identities and the values you get from the unit circle.

[@abdullahsumait7750]

i dont know what i would do without you 1000T*ThankYou

[@profrobbob]

+Abdullah Sumait you're welcome...just keep sharing my channel with everyone and remind them to like, subscribe and share their favorite educational channels to help us keep growing and remain free for others:D

[@profrobbob]

I am sorry, but right now I am just trying to stay ahead of my Geometry class...a new topic I am teaching this year along with 3 other subjects. I am also starting to plan for Calculus next year. I hope you find the proofs you need, but I cannot help right now.

[@donkunyung]

you are the best teacher ever. thank you. my math teacher sucks. and your videos are actually very interesting and fun. thank you. so much. :)

[@jamiesong01]

this is the topic on our trig now... i really don't understand what our prof discussed. now I've realized that this lesson is fine :D thank you :))

[@profrobbob]

You're welcome YouMe Park and thanks for liking, subbing and learning from #ProfRobBob !

[@caitlinbencsko4699]

So simple when hearing and seeing it being explained like this! Thank you so much! Glad to have come across your channnel

[@profrobbob]

+Caitlin Bencsko You are so welcome and thanks for studying and subbing and please tell all your friends, class and teachers to watch and do the same:D

[@dominiquerodriguez5686]

Thank you so much!! It's people like you that help me get through high school!!!

[@profrobbob]

You're welcome...thanks for liking and watching but please help support by sharing and SUBSCRIBING:)

[@profrobbob]

Thank you:D I appreciate you watching.

[@profrobbob]

If you go to my channel's home page and then select one of the playlists...they will be in the order I teach...unless I made an error:)

[@profrobbob]

THANK YOU!...and thanks for choosing Tarrou's Chalk talk to watch and learn from!

[@KevinLopez-ly3qz]

This video was well done helped me out so much! We just started this part in class but did not get to go into detail before the weekend. I wanted to get a jump start on homework and this video brought it all together for me. Thank you for taking your time to make and post this video much appreciated!!!

[@profrobbob]

You're welcome...and THANK YOU for taking the time to look for help, choose my channel to learn from, sub, and to thank the teacher !

[@profrobbob]

I am sorry, but my work schedule at school is making it very difficult for me to answer all the math questions I am receiving on KZbin at the moment or make extra example videos. I hope you get the answer you need. I am trying to stay ahead of my new Calc class as well teach 3 other subjects at once:(

[@profrobbob]

I love being an on-line "SUPER" helpful hero! Thanks for watching and please share with your friends:D

[@edwardhaughney9665]

Congrats BAM Man, thanks for the videos. Like the directness and speed with which you get to the point. Thanks for the addition of the light bulbs and keep mixing it up. Best to you.

[@profrobbob]

+Edward Haughney you're welcome! Seven months and still watching and supporting...THANK YOU!

[@musicluvrnicky]

Did anyone else get scared when he jumped in? Yeah. I did.

[@profrobbob]

+Nicky Magallon must be your first video...lol You'll get used to it after you like, subscribe and learn some more:)

[@sahiltalwar1101]

+ProfRobBob pfffft she must be new

[@GauravGRocks]

Yep, I did as well

[@profrobbob]

keep watching...you'll get used to it...BAM!!!

[@knucklechukka]

I can't say thank you enough Pearson mathlab only helps so far.

[@profrobbob]

knucklechukka Thank you for choosing my lessons to learn from!!! Are you taking an online class or just have the Pearson mathlab as a extra resource for your traditional class?

[@knucklechukka]

ProfRobBob Pearson is the program our classes homework is done (trig/coll alg) sometimes it has a tendency to be lacking in explanation on its steps

[@profrobbob]

I did not just work cosine, I recognized the expression matched the right side of the difference identity of cosine...and then applied that identity

[@profrobbob]

I have better skills now:) I do my videos now with a dedicated video recorder in manual mode with a much better microphone too. I hope you still find my early videos helpful.

[@TheRosaroonie]

ProfRobBob, I'm so thankful for all of your videos! They really help me understand the concepts! I told my trig class about your channel and website & hope they all check it out! *doing my homework!* :)

[@profrobbob]

+Rose A that's AWESOME!!! You make this teacher proud:) We are also thankful for students like you who take the time to share these free educational channels...please remind them too, how important it is to like, subscribe, share with friends, students and teachers and thru all forms of social media because thats the only way most of these free channels continue to grow and remain free for everyone:D

[@mamu7mich]

no problem. I found the proof on youtube. you have a great channel. keep up the good work.

[@akshaysambandham332]

Thank you very much Mr. Torrou! I was preparing for my Pre calc final exam over the past week and referenced your videos a lot! Very useful!! Bam!!

[@profrobbob]

Akshay Sambandham you're welcome! Thanks for studying with my channel too, keep spreading the word :D

[@akshaysambandham332]

Just got results back from the county for my PreCalculus exam. Got the highest grade in my class! Thank you so much Mr. Torrou!

[@profrobbob]

Akshay Sambandham BAM!!! You're welcome and thanks for studying! Also, CONGRATULATIONS and I hope you told your teacher about my channel so they could share it with future students:D

[@profrobbob]

I'm sorry, not that I know of...I have never loaded captions with my videos:( Maybe you can find somewhere else to watch it...but thanks for inquiring.

[@josephmajorczak272]

Thank you for saving my trig grade

[@HeartsWake_RS]

Only if my teacher had your charisma, i feel like i'm falling behind and this video picked me back up and i'm ready to do more math! :D

[@profrobbob]

BAM!!! Kyle Ludwig Thanks for the compliment and I hope my videos continue to keep you inspired and motivated to "do more math"...then when you have filled your brain full of math, you can share your learning experience and like, subscribe and share my channel with all your friends, classmates and teachers too:D