Sum and Difference Identities & Formulas - Sine, Cosine, Tangent - Degrees & Radians, Trigonometry

This trigonometry video tutorial explains how to use the sum and difference identities / formulas to evaluate sine, cosine, and tangent functions that have angles that are not commonly found in the unit circle. Examples include angles both in degrees and radians.
Bearing Problems and Navigation:
• Bearing Problems & Nav...
Two Triangle Problems - More Examples:
• Trigonometry - How To ...
Verifying Trigonometric Identities:
• Verifying Trigonometri...
Double Angle Identities:
• Double Angle Identitie...
Verifying Trig Identities With Double Angles:
• Verifying Trigonometri...
__________________________
Half Angle Formulas:
• Half Angle Formulas & ...
Verifying Trig Identities Using Half Angles:
• Verifying Trigonometri...
Inverse Trig Functions With Double Angles:
• Inverse Trig Functions...
Right Triangle Trig With Half Angle Identities:
• Right Triangle Trigono...
Product To Sum + Sum to Product Formulas:
• Product To Sum Identit...
______________________________
Solving Trig Equations - Finding All Solutions:
• Solving Trigonometric ...
Solving Trig Equations With Multiple Angles:
• How To Solve Trigonome...
Solving Trig Equations With Double Angles:
• Solving Trigonometric ...
Trigonometry Final Exam Review:
• Trigonometry Final Exa...
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 422

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor7 ай бұрын

    Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Evaluating Inverse Trig Functions: kzread.info/dash/bejne/paNttsykZqrHYrg.html Verifying Trigonometric Functions: kzread.info/dash/bejne/gHlq3MWDg73OiJM.html

  • @corncobb2059
    @corncobb2059 Жыл бұрын

    who else here because their teacher can't teach

  • @AnnabelleDsouza

    @AnnabelleDsouza

    2 ай бұрын

    a year later but im here

  • @user-op4bc9ui5n

    @user-op4bc9ui5n

    Ай бұрын

    Same

  • @realking4918
    @realking49186 жыл бұрын

    cant wait til the semester is over

  • @PHILLYMEDIC69

    @PHILLYMEDIC69

    5 жыл бұрын

    same dude. I wanna die. Jsut wanna finish my exams

  • @sarinarahman2806

    @sarinarahman2806

    5 жыл бұрын

    Ahh dont worry.We are in this shit together.Lets show them

  • @King-hs9zc

    @King-hs9zc

    4 жыл бұрын

    Same

  • @heberdo4639

    @heberdo4639

    4 жыл бұрын

    same

  • @hamzab2404

    @hamzab2404

    2 жыл бұрын

    same

  • @inebriationconversation4526
    @inebriationconversation45265 жыл бұрын

    Im cramming for an exam and i just wanna thank you cuz you've consistently helped me learn these ancient evil spells known as trig

  • @firstlast5630

    @firstlast5630

    5 жыл бұрын

    My Trig test is tomorrow I literally want to fucking die... 4 pages of formulas to memorize I am so fucked.

  • @TheCyberSatyr

    @TheCyberSatyr

    4 жыл бұрын

    @@firstlast5630 I think trig is fun lol. Strangely. It's frustrating sometimes, but it's not as hard as some of the shit in algebra

  • @firstlast5630

    @firstlast5630

    4 жыл бұрын

    @@TheCyberSatyr I think it's way harder than Algebra. I made a c on the test and a b in the class btw... not that bad.

  • @TheCyberSatyr

    @TheCyberSatyr

    4 жыл бұрын

    @@firstlast5630 I barely made an A in algebra and am making a B in precal. Mostly because I wasn't prepared for my first exam and my instructor doesnt seem to like me (I never show up because its not mandatory and I feel like hes holding it against me via giving me the review late, wrong answers on the review, etc). Its annoying when you check his answers on the internet and find out that you're right and all of his choices are wrong. Other than my terrible instructor, I'm enjoying the course

  • @lopkobor6916

    @lopkobor6916

    4 жыл бұрын

    @@TheCyberSatyr im in calc but im here bc i dont remember some of these identities... boy trig identities sure are fun!

  • @thefakebro.s8643
    @thefakebro.s86437 жыл бұрын

    Deserves the diamond play button

  • @insiya4561

    @insiya4561

    6 жыл бұрын

    NO!! HE NEEDS THE PLACE OF PEWDIEPIE; the ruby play button

  • @articnexas2548

    @articnexas2548

    4 жыл бұрын

    U know what, I will say a emerald play button

  • @lepos4136

    @lepos4136

    3 жыл бұрын

    Lol no, he needs a Sapphire play button

  • @ethanhayes1123

    @ethanhayes1123

    2 жыл бұрын

    @@lepos4136 Lapis play button

  • @lepos4136

    @lepos4136

    2 жыл бұрын

    @@ethanhayes1123 an average Minecraft lover huh?

  • @adycarmona8486
    @adycarmona84864 жыл бұрын

    This corona virus ain’t it lmao but we still need that grade 😔✊🏻

  • @volarearicelli9286

    @volarearicelli9286

    4 жыл бұрын

    aight someone here gets it

  • @benji6596

    @benji6596

    4 жыл бұрын

    Lmao nah fr

  • @adansalgado7335

    @adansalgado7335

    4 жыл бұрын

    here for the same reason

  • @ReversePrimeOFFICIAL

    @ReversePrimeOFFICIAL

    4 жыл бұрын

    Just use Mathway

  • @brayton6683

    @brayton6683

    4 жыл бұрын

    Same here really hard now staying focused and studying and not really having classes but I'm glad we have them to help in this Hardship 😪🔥🔥😫

  • @JJSmalls
    @JJSmalls7 жыл бұрын

    You explained this section better than my textbook did.

  • @blackoutemzz2674

    @blackoutemzz2674

    5 жыл бұрын

    Trust me

  • @danielcohen2138

    @danielcohen2138

    5 жыл бұрын

    The textbooks are fucking shite. They don’t explain anything and if you don’t already have a thorough base knowledge on the subject you can forget about understanding the questions

  • @sanya5538

    @sanya5538

    5 жыл бұрын

    That's hardly surprising.

  • @blandinus_8683

    @blandinus_8683

    3 жыл бұрын

    completely agree mate its a chore to even try and make sense of what the text book is trying to explain if you dont already know the topic

  • @ngndnd

    @ngndnd

    3 жыл бұрын

    @@danielcohen2138 im mad af because these professors want you to spend hundreds on a textbook that you will never even look at. KZread is my textbook.

  • @jojibot9193
    @jojibot91935 жыл бұрын

    Khanacademy is good but when it comes to triggo this guy is king

  • @thedragon9326
    @thedragon93264 жыл бұрын

    Anyone else learning this during the coronavirus quarantine?

  • @shahzaibjaved8341

    @shahzaibjaved8341

    4 жыл бұрын

    bro i hate this class but yea

  • @rohanwazir5604

    @rohanwazir5604

    4 жыл бұрын

    Yeah

  • @milkcabbage1217

    @milkcabbage1217

    4 жыл бұрын

    Yooo I hate this 👌😎

  • @shortvideolovers6022

    @shortvideolovers6022

    4 жыл бұрын

    Me

  • @nerdbr0-758

    @nerdbr0-758

    3 жыл бұрын

    Ye

  • @jasonhess9307
    @jasonhess93074 ай бұрын

    You have allowed me to maintain a 3.7 gpa while working full-time and taking 16 hours a semester. You have singlehandedly taught me more than any teacher I have ever had. Thank you for your kindness and knowledge.

  • @mariyahyisrael5598
    @mariyahyisrael55985 жыл бұрын

    you are the reason I almost got 100% on my college exam, best teacher ever

  • @Wonder.house7
    @Wonder.house74 жыл бұрын

    finally you're speaking in a language I understand...thank you

  • @randallmcgrath9345
    @randallmcgrath93453 жыл бұрын

    No one: O-chem Tutor, "I'm about to save this man's whole career."

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    @yesimkhanh99325 жыл бұрын

    PAST 2 YEARS I HAD WATCHED ALL UR VIDEOS ABOUT MATH AND MY MATH GRADES ARE IMPROVED FROM C TO A, MY SCORE ON MATH SECTION IS 780 AND THIS ALL BCS OF U THX U

  • @chithomas972
    @chithomas9725 жыл бұрын

    You really are the organic tutor. You explained everything clearly like it is ABC. Thank you

  • @nikkiblair7625
    @nikkiblair7625 Жыл бұрын

    Thank you for helping me pass precalculus. Your videos are soooooo helpful and I prefer them over the ones given for my course. You're always so thorough and your instructions and steps are clear and easy for me to follow! I literally refer to your videos anytime I start a new lesson in precal.

  • @yessielito10
    @yessielito107 жыл бұрын

    thank you! this is the only video that helped me out!

  • @_TheSplicer_
    @_TheSplicer_5 жыл бұрын

    THANK YOU THANK YOU THANK YOU. You have helped me so much. My teacher uses the complex vocab and screws me up. I love how you make this so simplistic.

  • @elkc4355
    @elkc4355 Жыл бұрын

    I love this guy. Makes math as simple as studying any other course

  • @raqad4642
    @raqad46422 жыл бұрын

    You saved my life although my instructor kept giving us complicated questions, she kept tricking us. I wouldn’t pass the class without you 🤟 thanks 🙏

  • @mukhammedabusuveilim3468
    @mukhammedabusuveilim34685 жыл бұрын

    If I need to review something for my honors calc or hon chem I immediately come here! What a great man!

  • @joshuakwan2459
    @joshuakwan24595 жыл бұрын

    THANK YOU UR THE BEST! This was so helpful! Saved me cause I was sick and missed this in class.

  • @leah3482
    @leah34823 жыл бұрын

    you have no idea how much you've helped so many people

  • @julianrose7295
    @julianrose72955 жыл бұрын

    Khan Academy who?? Seriously though thank you for these videos!! My textbook is incomprehensible so this is a lifesaver

  • @haileymfelt

    @haileymfelt

    4 жыл бұрын

    Julian Rose factssss

  • @tmann986
    @tmann9863 жыл бұрын

    Wow! I did not think of converting the radian into degrees! That helps so much!

  • @GooseWasTakenWasTaken
    @GooseWasTakenWasTaken2 жыл бұрын

    Thankyou so much dude, my math teacher really sucks at teaching and this is helping me a lot

  • @nomanrafique1
    @nomanrafique15 жыл бұрын

    You are such an excellent teacher, Than you.......

  • @jaeen7665
    @jaeen76652 жыл бұрын

    JG coming through in the clutch once again. Your video is helping people nearly 6 years after posting.

  • @darian5672
    @darian56726 жыл бұрын

    The two triangles actually helped me to understand the unit circle so much better. Thank you!

  • @fbloorg6140
    @fbloorg61403 жыл бұрын

    I swear I can understand the lesson *More Clearly* watching this dude's videos, than listening to my teachers Lectures.

  • @drewtolar1318
    @drewtolar13186 жыл бұрын

    Your videos always help if I don't understand what's going on. Thank you

  • @darelantonio9114
    @darelantonio91142 жыл бұрын

    Wow thanks for the lesson , I have been struggling with the radian part

  • @danelmasambo2457
    @danelmasambo24576 жыл бұрын

    Thanks for having good lecturer like you.u r helping many.⛄⛄⛄⛄⛄⛄

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    @beatricecajetan26324 жыл бұрын

    aaaah,i love this channel,thank you!!! always coming thru for folks like myself.

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    @arrivedercilol1599 Жыл бұрын

    Thank you so much I literally won't survive without you.

  • @xandertroche44
    @xandertroche443 ай бұрын

    You’re so talented. Thank you man, may God bless you abundantly!!

  • @uldaricoloayon440
    @uldaricoloayon4404 жыл бұрын

    Your so organic no chemical its pure and helpful

  • @samadhisandunika302
    @samadhisandunika3022 жыл бұрын

    Trigonometry lesson so hard to me but after watch your video. I could solve my problem thank you so much.👍😀

  • @nerdybird5764
    @nerdybird57644 жыл бұрын

    Dude thank you so much. This is helping me pass my classes

  • @mitchellfamily90
    @mitchellfamily905 жыл бұрын

    fantastic explanations EVERYTIME!!

  • @catvyhuynh7359
    @catvyhuynh73596 жыл бұрын

    Thank you so much, your video will be my life saving in my test. Your explanations are not only simple and but your math presents are also easy to understand. I hope you would make more of these useful videos to help everyone with their math problems. Love your video :)

  • @TheTruthIsInTherePodcast
    @TheTruthIsInTherePodcast6 ай бұрын

    dude literally helped me go from a d to a a by the end of the year, your literally saving my butt!!!!!!!!!!!!

  • @mathsaplus932
    @mathsaplus9324 жыл бұрын

    God bless you Sir you the one making my e-learning effective

  • @chrislee7325
    @chrislee73255 жыл бұрын

    This whole 7.1, 7.2, 7.3, 7.4, 7.5 is stupid. It looks very easy, but when I start to do it this makes me crazy. WT

  • @khwahishjain8568

    @khwahishjain8568

    3 жыл бұрын

    sameee

  • @JunchenDesigns
    @JunchenDesigns5 жыл бұрын

    saved my life! thank you!

  • @dimpsydoligas7921
    @dimpsydoligas79216 жыл бұрын

    Thank You So Much Man I love the way you teach

  • @alant.j5030
    @alant.j50302 жыл бұрын

    YOU MAKE IT LOOK SOOO SIMPLE . THANK YOU SIR ! AM GETTING A DISTINCTION

  • @TheATLTengu
    @TheATLTengu4 жыл бұрын

    Kinda funny to see that even during quarintine, we are all still struggling to learn this the same as when we were in school.

  • @dormi_torio

    @dormi_torio

    3 жыл бұрын

    It's not like quarantine made me any smarter

  • @RumpelStiltskindarkone

    @RumpelStiltskindarkone

    2 жыл бұрын

    @@dormi_torio it should have made us smarter but we're to busy tryna understand this useless shit

  • @nailahhenderson5672
    @nailahhenderson56723 жыл бұрын

    It was very hard for me to memorise the SOH CAH TOA surd form from the circle but with the triangle is wayyyyyy easier. I love your channel.

  • @zamanmackan97
    @zamanmackan974 жыл бұрын

    Nice and clearly good explained 😁,thanks to you

  • @casscassmc
    @casscassmc4 жыл бұрын

    Amazing wonderful beautiful it’s slow clear thorough great video to watch after a breakdown

  • @MilesLeslie
    @MilesLeslie3 жыл бұрын

    Who else is learning this right now in Math? You got this!!❤

  • @rafaeledits8419
    @rafaeledits84193 жыл бұрын

    Hello! Just a question. For 17:07, can I just choose between any two angles in the unit circle that would sum up to 345 degrees? Or is there some basis/criteria that is needed to be followed? Thanks in advance.

  • @machmacker

    @machmacker

    2 жыл бұрын

    they have to be angles that you know of from the unit circle, you can do 300 and 45, 210 and 135, etc. but it wouldn't be helpful to use 200 and 145 since we don't know those from the unit circle

  • @hueeeeeeeeee
    @hueeeeeeeeee6 жыл бұрын

    This is the Shaw shank redemption of math problems. It’s beautifully done.

  • @Joeydoesmedicine
    @Joeydoesmedicine5 жыл бұрын

    I guess you are just going to teach me every subject, lol I watch your chem videos for gen chem 2

  • @herby_5481
    @herby_54812 жыл бұрын

    This was very helpful thank you!!

  • @SAIFKHAN-sn9su
    @SAIFKHAN-sn9su5 ай бұрын

    you’re a lifesaver fr🙏🏻

  • @linuxsport
    @linuxsport3 жыл бұрын

    This channel trig videos are on point.

  • @noneofyourbusinessboy7118
    @noneofyourbusinessboy71184 жыл бұрын

    Test two is coming up for me and the quarter is almost over. I need some motivation

  • @ignatiusmbo1769

    @ignatiusmbo1769

    4 жыл бұрын

    Prayer is the keyy

  • @deathraydave

    @deathraydave

    4 жыл бұрын

    We got this bois

  • @kennethhowell5291
    @kennethhowell52913 жыл бұрын

    You are the best! Thank you very much!

  • @evanbrant8022
    @evanbrant8022 Жыл бұрын

    Inthink what makes this dude so much better than professors at school is becuase he doesn’t mind going back to show you stuff you should have already known or have already been taught. But this dude doesn’t skip steps he goes full detail. Love it, wasting money and time in school. My community college “professor” constantly brags about his real university students, skips steps ALL the time, and then NEVER replies to emails. He’s even having us do assignments on stuff that he says we won’t have time to go over. TF?! Reporting him the second I’m done learning all the material he should have taught.

  • @raymondhenneh3521
    @raymondhenneh3521 Жыл бұрын

    Anytime I come to learn online I search for you first Best teacher

  • @okiemuteabe3331
    @okiemuteabe33312 жыл бұрын

    Ur such a life saver

  • @lucyginzel
    @lucyginzel2 жыл бұрын

    bro ur a lifesaver

  • @jamcaimen8768
    @jamcaimen87684 жыл бұрын

    Thank you for helping me with kumon

  • @TheCyberSatyr
    @TheCyberSatyr4 жыл бұрын

    If you memorize the unit circle, you always have access to it lmao. Cant wait for calc 1

  • @ejeguono1254
    @ejeguono1254 Жыл бұрын

    Great Job... May God bless you.

  • @ThatGuy-ws7gu
    @ThatGuy-ws7gu6 жыл бұрын

    Thank you so much this helped me alot

  • @lowopelumi207
    @lowopelumi207 Жыл бұрын

    Thank you. This is helpful 🥺❤️

  • @fintea9041
    @fintea90414 жыл бұрын

    You are the best!! Bless you!!

  • @fikkyd
    @fikkyd4 жыл бұрын

    if we had a large angle such as tan 345 couldn't we just find the coterminal angle and subtract 2 pi or 360 from thus not having to use the reference angles?

  • @ruhi4985
    @ruhi49857 жыл бұрын

    thanks man you saved my maths grade

  • @joyflanagan7722
    @joyflanagan77225 жыл бұрын

    Finally a helpful tutorial

  • @lhanceandrewtambis9839
    @lhanceandrewtambis98396 ай бұрын

    Easy to understand fr..❤

  • @sethnary3974
    @sethnary3974 Жыл бұрын

    At 10:44 is there anything wrong with doing tan(60-45) or should I learn to use the lowest possible combination for good practice?? Just wondering if there is any difference?

  • @labanmupendah4222
    @labanmupendah42222 жыл бұрын

    Excellent explanation. This is the topic in which I have been facing challenges for the past 3years. Thanks very much for your help 🙏

  • @noura3431
    @noura34312 жыл бұрын

    Thank you so much !!

  • @martinmaina523
    @martinmaina5234 жыл бұрын

    thank you for the tutoring.you are doing a great job.just to confirm,is tan 30 root 3/3 really from the special triangles

  • @tankfoman437
    @tankfoman4374 жыл бұрын

    I’ve been enlightened ☀️

  • @amagiyaisaiah692
    @amagiyaisaiah6927 ай бұрын

    Thanks this among the course content for maths 101 am doing.I'm a student from a Nigerian university 🇳🇬

  • @ruthrobb2384
    @ruthrobb23844 жыл бұрын

    What program are you using. I love it. You do a great job. I have to do videos for my classes and I get so nervous doing them.

  • @corey333p
    @corey333p5 жыл бұрын

    I don't get why the length of the hypotenuse at 5:00 does not equal 1. The hypotenuse = 1 on the unit circle, correct?

  • @monkeygirl4160
    @monkeygirl41605 жыл бұрын

    more helpful than my prof lol!!!

  • @seaamoeba3343
    @seaamoeba33434 жыл бұрын

    this man just changed the ENTIRE game

  • @essiamegbeto2681
    @essiamegbeto26816 жыл бұрын

    I thought that the angles that make up theta must be common angles eg. 30, 45, 90. In order to see it on the unit circle, but by this video it means that you just calculet it towards the x axis.

  • @vladimirmoravek2646
    @vladimirmoravek26465 жыл бұрын

    [15:35/21:44] Mark, tan(23pi/12) = tan(2pi-pi/12) = tan(-pi/12) = -tan(pi/12) = (3)^(1/2) - 2. (per previous example)

  • @LukePaciocco
    @LukePaciocco4 жыл бұрын

    14:43 .... I've coined this phenomena as "Einstein fog"... when you're so used to solving exponentially more intricate and tedious mathematic equations, only to return to something like basic division - it takes a moment for your brain to recalibrate to such a basic way of thinking. I noticed from the brief pause and "uhh". Einstein himself was incredibly guilty of this to a point where he'd even forget elementary equating.

  • @azimuth011

    @azimuth011

    4 жыл бұрын

    I can relate to this, a lot. I can solve a lot of complicated equations without calculator, only to use calculator for simple and basic operations like addition

  • @LukePaciocco

    @LukePaciocco

    4 жыл бұрын

    @@azimuth011 I was INSANELY in the zone studying, super caffeinated up, and being my typical over-analytical self when I wrote that comment, hahaha. So funny coming back to read it. I'm glad you could relate, Kira. Because regardless, this experience is absolutely a real thing! 😁

  • @quantumwave1036

    @quantumwave1036

    4 жыл бұрын

    I won't lie there have been times where I have run simple addition into my calculator because I wasn't so sure of such a simple answer.

  • @user-gm9ph9iv2j
    @user-gm9ph9iv2j6 ай бұрын

    thank you your tutorials are awesome I have a question though how do you find the coordinate of intersection when a cosine and sine intersect by equating the two functions equations this type of question was in my recent math exam

  • @brayton6683
    @brayton66834 жыл бұрын

    I'm so glad school are opening soon this staying at home not really having classes is killing me . I'm really losing focus at the task at hand which is school and studying like staying at home just makes me more lazier 😥

  • @brooktekie1281
    @brooktekie12817 жыл бұрын

    My man, Thank uuuuuuuuuuuuuuuuuuuu! bless.

  • @elhadmuharemovic5870
    @elhadmuharemovic58706 жыл бұрын

    Thank you Mark Whalberg

  • @user-zz1tp2mo4c

    @user-zz1tp2mo4c

    6 жыл бұрын

    Marky Mark and The Funky Math

  • @namemanguy
    @namemanguy2 жыл бұрын

    Good vid dude

  • @dhirajthapa5797
    @dhirajthapa57973 жыл бұрын

    LIFE SAVER

  • @justinliebenberg2321
    @justinliebenberg23214 жыл бұрын

    Thanks.. Helped me a lot... Please make a more detailed video with harder examples like "write cos(arctan+arccosx) as an algebraic expression", proving a cofunction identity, deriving reduction formulas, and verifying using sum and difference formulas. Would be a great help

  • @9zero187

    @9zero187

    2 жыл бұрын

    My dude, I would shit my pants

  • @levioffner
    @levioffner3 жыл бұрын

    Thank you so much!

  • @mohammedalmikail420
    @mohammedalmikail4204 жыл бұрын

    Thank you so much!! helped me a lot

  • @gracediama6302

    @gracediama6302

    4 жыл бұрын

    Mohammed AlMikail so you going through quarantine to huh 😭

  • @mohammedalmikail420

    @mohammedalmikail420

    4 жыл бұрын

    @@gracediama6302 yep :( and daily math quizzes aren't helping lol

  • @okiemuteabe3331
    @okiemuteabe33312 жыл бұрын

    Keep up d good work

  • @alyhaywood8841
    @alyhaywood88413 жыл бұрын

    I appreciate you so much.

  • @chandlercopenhaver5659
    @chandlercopenhaver5659 Жыл бұрын

    i owe you my life

  • @saki7952
    @saki79522 жыл бұрын

    Thanks a lot

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