All of Trigonometric Identities and Equations in 30 minutes!! | Chapter 10 | A level Pure Maths

A video revising the techniques and strategies required for all of the AS Level Pure Mathematics chapter on Trigonometric Identities and Equations that you need to achieve a grade C-A* in your A-Level Pure Maths.
These topics are the essential question styles that appear in the Trigonometric Identities and Equations Module. This however is not ALL of the question styles within the A-Level. Further videos can be found on the channel for a more in depth look at some of these topics.
👑 Everything you Need to Pass your AS Pure Maths Exam! A* | AS Pure Maths Revision | Edexcel AQA & OCR - • Everything You Need to...
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See below for further links to each of these topics:
See below for more chapter based revision videos:
Chapter 1 - Algebraic Expressions - • All of Algebraic Expre...
Chapter 2 - Quadratics - • All of Quadratics in 4...
Chapter 3 - Equations and Inequalities - • All of Equations and I...
Chapter 4 - Graphs and Transformations - • All of Graphs and Tran...
Chapter 5 - Straight Line Graphs - • All of Straight Line G...
Chapter 6 - Circles - • All of Circles in 25 M...
Chapter 7 - Algebraic Methods - • All of Algebraic Metho...
Chapter 8 - Binomial Expansion - • All of Binomial Expans...
Chapter 9 - Trigonometric Ratios - • All of Trigonometric R...
Chapter 10 - Trig Identities and Equations - • All of Trigonometric I...
Chapter 11 - Vectors and Magnitude - • All of Vectors and Mag...
🔹 Watch the video
🔹 Make notes
🔹 Practice the questions
🔹 Mark your work
🔹 Review what you have learnt on the exam questions
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00:00 Intro
01:22 Trigonometric Graphs
03:30 Exact values
04:37 Trigonometric Identities
06:46 Proving Trigonometric Identities
12:57 Solving Trigonometric Equations
22:41 Solving Harder Trigonometric Equations
36:07 Outro
Enjoy the video!
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Пікірлер: 144

  • @TheGCSEMathsTutor
    @TheGCSEMathsTutor2 жыл бұрын

    👑 Everything you Need to Pass your AS Pure Maths Exam! A* | AS Pure Maths Revision | Edexcel AQA & OCR - kzread.info/dash/bejne/h51_uKSsmKy1ppc.html If anyone would like to support the channel you can become a member here: kzread.info/dron/StPzCGyt5tlwdpDXffobxA.htmljoin or buy me a coffee here: www.buymeacoffee.com/gcsemathstutor Thank you for all of your support! 😁🙏🏼 New Discord Link: discord.gg/nRMtgr5AWA 👑

  • @bastianjohnson6645

    @bastianjohnson6645

    2 жыл бұрын

    Hi I wanted to tell you there seems to be a mistake at 27:14 question as it wouldn't be possible for to get 4-5cos theta

  • @jacobmcgrory2841
    @jacobmcgrory2841 Жыл бұрын

    ive had enough

  • @hemragulyusuf4069

    @hemragulyusuf4069

    7 ай бұрын

    Real

  • @AbdulHadi-ud8dj

    @AbdulHadi-ud8dj

    6 ай бұрын

    bruh same

  • @liza.56

    @liza.56

    6 ай бұрын

    Same

  • @josephabraham1848

    @josephabraham1848

    6 ай бұрын

    Real

  • @Ayzlxn

    @Ayzlxn

    6 ай бұрын

    So real

  • @stannersindustries4985
    @stannersindustries49852 жыл бұрын

    I don't understand how these videos are not more popular! You are doing a true service for the good maths education with these videos. (Particularly A-Level, these are much better than the competition).

  • @tejeshvararunkumar9411
    @tejeshvararunkumar9411 Жыл бұрын

    I used his videos so much for my GCSEs and I am confident in saying he is one of the reasons to how I got an 8. I didn't he made A level videos and I have been struggling without his help till now. I am doing far better now thanks to you

  • @TheGCSEMathsTutor

    @TheGCSEMathsTutor

    Жыл бұрын

    I’m so glad to hear I could help! Amazing news on your GCSE grade keep up the amazing work! I’m working on some more A-Level videos over the holidays! 😁🙏🏼

  • @tanirsethu5662
    @tanirsethu5662 Жыл бұрын

    Thanks a lot man 🙏. I tried to learn this so many times and couldn't understand it but now you taught me the method my a level maths teachers could never teach. If it wasn't for you, I would be failing a level maths. God bless you

  • @shakz7
    @shakz72 жыл бұрын

    Thanks my g, really helped with my A Level maths

  • @sebclaye9326

    @sebclaye9326

    Жыл бұрын

    same here g appreciate it mush

  • @courtneylust

    @courtneylust

    Жыл бұрын

    really? what grade did you get?

  • @shakz7

    @shakz7

    Жыл бұрын

    @@courtneylust Icl I got excluded from my old sixth😭, I go to a colly now and im predicted A wbu

  • @lukesampson8181

    @lukesampson8181

    Жыл бұрын

    @@shakz7why’d u get excluded lmaooo

  • @shakz7

    @shakz7

    Жыл бұрын

    @@lukesampson8181 Dw😂

  • @davidhill8163
    @davidhill81632 жыл бұрын

    Many thanks for breaking this down slowly and step by step

  • @katherinemb.6308
    @katherinemb.63082 жыл бұрын

    Oh my god this helped so much. Thank you thank you thank you. Really appreciate your work and channel.

  • @Jetset_hd
    @Jetset_hd2 жыл бұрын

    extremely helpful, thank you so much

  • @tanatswadebwe8021
    @tanatswadebwe80212 жыл бұрын

    You got me a A 89% at IGCSE math 💓💓

  • @unknown-wm5ls
    @unknown-wm5ls2 жыл бұрын

    These videos are genuinely a life saver, thanks.

  • @alisonjalon13
    @alisonjalon13 Жыл бұрын

    this was so useful, thank you!

  • @vaed1651
    @vaed16514 ай бұрын

    video helped so much. I'm watching this in preparation for my further maths mock exaam and this has saved me.

  • @lizbasiita3498
    @lizbasiita3498 Жыл бұрын

    Thank you so much! Just one thing though: Have you considered using a thinner pen/marker for your whiteboard? I think it would just make your videos all the more perfect!🥰

  • @chocolate8818
    @chocolate8818Ай бұрын

    Lovely video! I finally understood this topic thanks to you sir.

  • @Bxbyjyyy
    @Bxbyjyyy5 ай бұрын

    I passed my IGCSE math with an A coz of this guys. Teachers were just waffling. Now I'm back for A level and he still the reason. I LOVE YOU MR TUTOR!!!!!!!!!

  • @malulu.9118
    @malulu.91188 ай бұрын

    this is really helpful thank you so much

  • @charliecampbell5598
    @charliecampbell5598 Жыл бұрын

    Thank you so much for this! The textbook uses the circle method but my teachers use this method - much simpler imo

  • @sanzusbbl9844
    @sanzusbbl98445 ай бұрын

    Sir please do more Alevel vidoes these are saving me !!! u lift soo much stress off my head

  • @apple6112
    @apple61123 ай бұрын

    12:09 you could also remove the 5 common from 5sin2theta + 5cos2theta to get 5(sin2theta+cos2theta) which is equivalent to 5

  • @immanuellaAyuk

    @immanuellaAyuk

    Ай бұрын

    that's the same thing i thought of

  • @AbdulMalik-qs9fg
    @AbdulMalik-qs9fg Жыл бұрын

    bro can you please make a playlist on AS topics for stats and mechanics? It would be extremely helpful

  • @marib5440

    @marib5440

    Жыл бұрын

    frrr do you know any good playlists for that

  • @azureass1661

    @azureass1661

    Жыл бұрын

    ​@@marib5440TLmaths is pretty solid imo

  • @smashaj2955

    @smashaj2955

    6 ай бұрын

    @@marib5440maths genie website is good

  • @SeoYejun-tf8dc
    @SeoYejun-tf8dc7 ай бұрын

    You are my life saver🎉

  • @jamie7707
    @jamie77072 жыл бұрын

    Thanks for this amazing video Sir! Is there any chance possible if you may go through the quadrant method used to solve trigonometric functions as that is another method used for solving trigonometric functions and equations sir. Thanks for producing these amazing helpful and straight to the point chapter videos 👍👍👍🔥🔥🔥

  • @tanatswadebwe8021
    @tanatswadebwe80212 жыл бұрын

    I love this guy I swear 😭😭😭

  • @straymite707
    @straymite7072 жыл бұрын

    Thanks so much this is really helpful for revision!

  • @tinashemangumba1169
    @tinashemangumba11692 жыл бұрын

    Thank you so much u really helped me

  • @Washingmachine256
    @Washingmachine2565 ай бұрын

    well i finally learnt how to factorise properly in this video ❤

  • @gracegrimwood5723
    @gracegrimwood57232 жыл бұрын

    are you going to do the statistics and mechanics?

  • @Henry-sp3ku
    @Henry-sp3ku2 жыл бұрын

    top quality mate

  • @whizzriz8139
    @whizzriz8139 Жыл бұрын

    Hey sir, can you do AS stats and mechanics as well?

  • @mohammedalharthy2789
    @mohammedalharthy2789 Жыл бұрын

    well done, thank you sir

  • @TheGCSEMathsTutor

    @TheGCSEMathsTutor

    Жыл бұрын

    You are very welcome!

  • @FuckerCummings
    @FuckerCummings10 ай бұрын

    Thanks very much man , ill be sure to share your channel with my friends , if only you did the full a level course

  • @IndigoRM
    @IndigoRM Жыл бұрын

    THANK YOU

  • @lemonadechilli172
    @lemonadechilli172 Жыл бұрын

    You saved my exam mate very helpful thank you a lot

  • @ippo5005
    @ippo50052 жыл бұрын

    Thank you

  • @jamespinder8381
    @jamespinder8381 Жыл бұрын

    In the solving trig equations chapter, using the quadratic method wouldn't you only get the first two answers? Because 57 and 122 fall into the A and S quadrants, and the other two values fall into the T and C quadrants?

  • @tombob641
    @tombob641 Жыл бұрын

    Why couldn’t you just factorise the 5sin^2 +5cos^2 >>> 5(sin^2+cos^2) >>>> 5(1) >>> 5, am I correct or?

  • @YashveerRamchurn-cs5xw

    @YashveerRamchurn-cs5xw

    10 ай бұрын

    Yeah, that works too cus I also did that and got the correct answer

  • @kola7483
    @kola74832 жыл бұрын

    banga vid like usual chap

  • @TheGCSEMathsTutor

    @TheGCSEMathsTutor

    2 жыл бұрын

    Thank you! Glad to hear it 😁🙏🏼

  • @jozimaps9420
    @jozimaps94202 жыл бұрын

    You are incredible

  • @TheGCSEMathsTutor

    @TheGCSEMathsTutor

    2 жыл бұрын

    Thank you so much 😁🙏🏼

  • @zoe.nothando
    @zoe.nothando Жыл бұрын

    thank you

  • @hi-pg9bp
    @hi-pg9bp Жыл бұрын

    Thanks

  • @Amir-nv6cs
    @Amir-nv6csАй бұрын

    At 11:00, could u not have factorised the 5 out of the equation? So that it would become 5(sin^2theta+cos^2theta). Then that becomes 5(1). Which becomes 5?

  • @jacklordeyey8546
    @jacklordeyey8546 Жыл бұрын

    22:10 I understand how you find 57.7 and 122.3 by doing the quadrant method but how do you find the other two values as aren’t the only two quadrants the a and in the cast diagram

  • @jamespinder8381

    @jamespinder8381

    Жыл бұрын

    exactly what i was thinking, theyre in the S and T quadrants

  • @user-vq4qy2hq5i
    @user-vq4qy2hq5i3 ай бұрын

    How important is the unit circle for AQA A Level Maths?

  • @gudforyou9103
    @gudforyou9103 Жыл бұрын

    25:55 i did not understand why you changed one of the minus signs to plus. isnt it supposed to stay minus?

  • @sugawaraaa9167

    @sugawaraaa9167

    4 ай бұрын

    He multiplied by minus 1 to make it easier and then swapped the numbers in the brackets at the end to make it the same as before

  • @numan4166
    @numan4166 Жыл бұрын

    For the 7sin squared = 5 question ( 3rd question) do we need to give the 4 x values because in the question for drawing the graph, it's asking from 0 to 360

  • @andymandy1909

    @andymandy1909

    Жыл бұрын

    I think you do because all 4 x values that he found lie between the intervals of 0 - 360.

  • @yopolis4523
    @yopolis45232 жыл бұрын

    I don,t understand the example where where we show the equation equals to 4-5 cos0. You changed the sign for the quadratics and when you found your 2 answers, you also changed the (5x-4) into (4-5x). The sign (-) follows the 4 not the 5 but you just swapped it. Can you please explain this part? I don’t understand it at all.

  • @yopolis4523

    @yopolis4523

    2 жыл бұрын

    Also, I didn’t change the quadratics sign so i got (-5cos0 + 4) (2cos0 - 3)/ (3 + 2cos0). Do the 3 +2cos0 and the 3 - 2cos0 cancel out? Please let me know if you see this comment.

  • @kamikazechameleon3700

    @kamikazechameleon3700

    2 жыл бұрын

    if you're talking about the quadratic at 28:32 its because the quadratic was originally negative and he made it positive so he had to change the output to expand out into the negative the quadratic instead of the positive

  • @user-qr2ni2sb1f
    @user-qr2ni2sb1f6 ай бұрын

    Sir please can we be solving GCE question More often??

  • @sassinemselabe1496
    @sassinemselabe14962 жыл бұрын

    nice video, but please bring in some more difficult trig identities next time

  • @asmaa1853
    @asmaa18532 жыл бұрын

    Thank you 💖💖

  • @antonytembo3120
    @antonytembo31207 ай бұрын

    Would you still get the same answers if you use different graphs ?32:25 for example instead of using the tan graph you use either the cos or sin graph?

  • @maryammm859

    @maryammm859

    7 ай бұрын

    no, ud have to use the graph for that particular function, e.g. tan graph for solutions for tan x = a

  • @leotang3242
    @leotang32422 жыл бұрын

    please do more pure maths video please!!!!

  • @ff_cobra_kai
    @ff_cobra_kai2 жыл бұрын

    Can I ask ...in the first example can we just factor out 5 Then turn everything into 1?

  • @dionthomas2967

    @dionthomas2967

    2 жыл бұрын

    No because you are trying to show that it’s identical to 5 so you shouldn’t really change the right side.

  • @arzaadkhan501

    @arzaadkhan501

    2 жыл бұрын

    @@dionthomas2967 but your not bringing anything to the right side. its 5(coa^2+sin^2)

  • @potati4097
    @potati4097 Жыл бұрын

    27:21 why wouldn't it be (3+2x)(-4+5x) because you need negative 12, so why would the 4 be positive??

  • @sugawaraaa9167

    @sugawaraaa9167

    4 ай бұрын

    Because he multiplied by minus 1 before factorising you have to switch the numbers in the brackets to make it the same quadratic

  • @mathsmeadow5106
    @mathsmeadow51062 жыл бұрын

    Is there any possibility that you would go through A2 pure maths before our exam 2022?

  • @chillvibes1748
    @chillvibes17482 жыл бұрын

    Hello sir at around 27:14 how can (5x-4) be written as (4-5x), do you rearrange to first get (-4+5x) and then multiply that by (-1) to get (4-5x)

  • @charliefowler2781

    @charliefowler2781

    2 жыл бұрын

    it's because he flipped the signs around earlier to make 10x^2+7x-12, so then he flipped the signs back around afterwards

  • @bastianjohnson6645

    @bastianjohnson6645

    2 жыл бұрын

    @@charliefowler2781 yes but that still gives you same factors but do you then after multiply by - 1

  • @MuhammedKhabbab
    @MuhammedKhabbabАй бұрын

    if sin^2θ + cos^2θ = 1 then 5sin^θ + 5cos^2θ = 5. isn't that the proof. both sides have been multiplied by 5

  • @dontclickonmyprofilepictur7561

    @dontclickonmyprofilepictur7561

    20 күн бұрын

    yh thats what i thought

  • @rissikesthiyagarajah2205
    @rissikesthiyagarajah22059 ай бұрын

    Thx

  • @jeffjeffson5967
    @jeffjeffson5967 Жыл бұрын

    27:05 Sir, what is happening in this section?

  • @TheGCSEMathsTutor

    @TheGCSEMathsTutor

    Жыл бұрын

    Factorising a negative quadratic! I have a video on that if you search the channel 😁🙏🏼

  • @jeffjeffson5967

    @jeffjeffson5967

    Жыл бұрын

    @@TheGCSEMathsTutor Thank you sir.

  • @Bxbyjyyy
    @Bxbyjyyy4 ай бұрын

    Dear Sir At 4:19 minutes, on the graph of exact trig values you wrote that cos45 and sin45 equal to 1 over root 2. They're both actually equal to root 2 over 2 Sir. Thank you very much more, I'm understanding the concepts coz of this vid!😊

  • @sugawaraaa9167

    @sugawaraaa9167

    4 ай бұрын

    1 over root 2 is equivalent to root 2 over 2

  • @mrcheese1373
    @mrcheese13732 жыл бұрын

    Thanks mate

  • @VBAHMED

    @VBAHMED

    2 жыл бұрын

    no problem

  • @AshFeynman

    @AshFeynman

    2 жыл бұрын

    @@VBAHMED you're welcome

  • @Sofia-gk9sn
    @Sofia-gk9sn2 жыл бұрын

    Hi Sir do you think you could cover the quadrant method please?

  • @sei7082
    @sei70822 жыл бұрын

    at 22:04 your method is very long and gives inaccurate values, on calculator go to MODE SETUP --> TABLE --> f(X) = sin(X) --> START? Type number on the left of X in the interval so that's 0 --> END? Type number on the right of X in the interval so that's 360 --> STEP? Type your value for X then the values will be shown in a table. you don't need a graphical calculator just something like the classwiz, saves time and is accurate

  • @tasangerbakes
    @tasangerbakes Жыл бұрын

    11:00 could u not just factor out the 5 and make what's inside the brackets equal to 1 then 5x 1 = 5 ?

  • @areefilyas8850
    @areefilyas88502 жыл бұрын

    W video

  • @badoublenana
    @badoublenana6 ай бұрын

    At 27:27 I had worked out the same way, but I don't get how (5x-4) becomes (4-5x).

  • @williambailey9343

    @williambailey9343

    5 ай бұрын

    Neither do I. Any explanation?

  • @sugawaraaa9167

    @sugawaraaa9167

    4 ай бұрын

    @@williambailey9343because he multiplied the quadratic by minus 1 before factorising so you have to swap the numbers in the brackets at the end

  • @sugawaraaa9167

    @sugawaraaa9167

    4 ай бұрын

    @@williambailey9343he swapped 2x + 3 to 3 + 2x as well even though it doesn’t matter

  • @williambailey9343

    @williambailey9343

    4 ай бұрын

    @@sugawaraaa9167 yeah thanks. I managed to understand it after some thinking. Just need to make one bracket negative as making both negative does nothing. If you make the other bracket negative it still cancels out.

  • @ethanmather465
    @ethanmather4655 ай бұрын

    17:00

  • @mistermusab8055
    @mistermusab80555 ай бұрын

    23:13

  • @Remus786
    @Remus7862 жыл бұрын

    How can 5x-4 be written as 4-5x 27:20

  • @riotza7597

    @riotza7597

    2 жыл бұрын

    cause remember he made -10x^2, 10x^2 to make it easier to work with so at the end he reversed what he did originally

  • @Ja-od1mh
    @Ja-od1mh4 ай бұрын

    Where’s r cos alpha vid

  • @BarniDeDino
    @BarniDeDino Жыл бұрын

    Gosh this chapter is annoying, your explanation helped tho, thanks man

  • @joey1317
    @joey1317 Жыл бұрын

    Never skip steps. It’s a bad habit to get into and loses marks in exams…

  • @roxc453

    @roxc453

    Жыл бұрын

    I rlly need to remember this but I keep thinking the examiner can read my mind or something

  • @courtneylust

    @courtneylust

    Жыл бұрын

    @@roxc453 lol same

  • @user-mx6hd7gg6k
    @user-mx6hd7gg6k7 ай бұрын

    Endless pain and suffering I am tired

  • @castor5580
    @castor558011 ай бұрын

    If this is a level maths me is whole alphabet 😂

  • @BobBob-uv9fq
    @BobBob-uv9fq Жыл бұрын

    3;30 mins in and no obviously

  • @26Uncovered
    @26Uncovered25 күн бұрын

    I'm so cooked

  • @nhlanhlafuzane3535
    @nhlanhlafuzane35352 жыл бұрын

    roasted

  • @geezer1024
    @geezer102425 күн бұрын

    tired

  • @Yamesy
    @Yamesy Жыл бұрын

    Thank you

  • @Amir-nv6cs
    @Amir-nv6csАй бұрын

    At 11:00, could u not have factorised the 5 out of the equation? So that it would become 5(sin^2theta+cos^2theta). Then that becomes 5(1). Which becomes 5?

  • @Amir-nv6cs
    @Amir-nv6csАй бұрын

    At 11:00, could u not have factorised the 5 out of the equation? So that it would become 5(sin^2theta+cos^2theta). Then that becomes 5(1). Which becomes 5?