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...
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🔹 Practice the questions
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🔹 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
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@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
ive had enough
@hemragulyusuf4069
7 ай бұрын
Real
@AbdulHadi-ud8dj
6 ай бұрын
bruh same
@liza.56
6 ай бұрын
Same
@josephabraham1848
6 ай бұрын
Real
@Ayzlxn
6 ай бұрын
So real
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).
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
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! 😁🙏🏼
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
Thanks my g, really helped with my A Level maths
@sebclaye9326
Жыл бұрын
same here g appreciate it mush
@courtneylust
Жыл бұрын
really? what grade did you get?
@shakz7
Жыл бұрын
@@courtneylust Icl I got excluded from my old sixth😭, I go to a colly now and im predicted A wbu
@lukesampson8181
Жыл бұрын
@@shakz7why’d u get excluded lmaooo
@shakz7
Жыл бұрын
@@lukesampson8181 Dw😂
Many thanks for breaking this down slowly and step by step
Oh my god this helped so much. Thank you thank you thank you. Really appreciate your work and channel.
extremely helpful, thank you so much
You got me a A 89% at IGCSE math 💓💓
These videos are genuinely a life saver, thanks.
this was so useful, thank you!
video helped so much. I'm watching this in preparation for my further maths mock exaam and this has saved me.
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!🥰
Lovely video! I finally understood this topic thanks to you sir.
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!!!!!!!!!
this is really helpful thank you so much
Thank you so much for this! The textbook uses the circle method but my teachers use this method - much simpler imo
Sir please do more Alevel vidoes these are saving me !!! u lift soo much stress off my head
12:09 you could also remove the 5 common from 5sin2theta + 5cos2theta to get 5(sin2theta+cos2theta) which is equivalent to 5
@immanuellaAyuk
Ай бұрын
that's the same thing i thought of
bro can you please make a playlist on AS topics for stats and mechanics? It would be extremely helpful
@marib5440
Жыл бұрын
frrr do you know any good playlists for that
@azureass1661
Жыл бұрын
@@marib5440TLmaths is pretty solid imo
@smashaj2955
6 ай бұрын
@@marib5440maths genie website is good
You are my life saver🎉
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 👍👍👍🔥🔥🔥
I love this guy I swear 😭😭😭
Thanks so much this is really helpful for revision!
Thank you so much u really helped me
well i finally learnt how to factorise properly in this video ❤
are you going to do the statistics and mechanics?
top quality mate
Hey sir, can you do AS stats and mechanics as well?
well done, thank you sir
@TheGCSEMathsTutor
Жыл бұрын
You are very welcome!
Thanks very much man , ill be sure to share your channel with my friends , if only you did the full a level course
THANK YOU
You saved my exam mate very helpful thank you a lot
Thank you
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?
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
10 ай бұрын
Yeah, that works too cus I also did that and got the correct answer
banga vid like usual chap
@TheGCSEMathsTutor
2 жыл бұрын
Thank you! Glad to hear it 😁🙏🏼
You are incredible
@TheGCSEMathsTutor
2 жыл бұрын
Thank you so much 😁🙏🏼
thank you
Thanks
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?
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
Жыл бұрын
exactly what i was thinking, theyre in the S and T quadrants
How important is the unit circle for AQA A Level Maths?
25:55 i did not understand why you changed one of the minus signs to plus. isnt it supposed to stay minus?
@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
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
Жыл бұрын
I think you do because all 4 x values that he found lie between the intervals of 0 - 360.
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
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
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
Sir please can we be solving GCE question More often??
nice video, but please bring in some more difficult trig identities next time
Thank you 💖💖
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
7 ай бұрын
no, ud have to use the graph for that particular function, e.g. tan graph for solutions for tan x = a
please do more pure maths video please!!!!
Can I ask ...in the first example can we just factor out 5 Then turn everything into 1?
@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
2 жыл бұрын
@@dionthomas2967 but your not bringing anything to the right side. its 5(coa^2+sin^2)
27:21 why wouldn't it be (3+2x)(-4+5x) because you need negative 12, so why would the 4 be positive??
@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
Is there any possibility that you would go through A2 pure maths before our exam 2022?
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
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
2 жыл бұрын
@@charliefowler2781 yes but that still gives you same factors but do you then after multiply by - 1
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
20 күн бұрын
yh thats what i thought
Thx
27:05 Sir, what is happening in this section?
@TheGCSEMathsTutor
Жыл бұрын
Factorising a negative quadratic! I have a video on that if you search the channel 😁🙏🏼
@jeffjeffson5967
Жыл бұрын
@@TheGCSEMathsTutor Thank you sir.
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
4 ай бұрын
1 over root 2 is equivalent to root 2 over 2
Thanks mate
@VBAHMED
2 жыл бұрын
no problem
@AshFeynman
2 жыл бұрын
@@VBAHMED you're welcome
Hi Sir do you think you could cover the quadrant method please?
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
11:00 could u not just factor out the 5 and make what's inside the brackets equal to 1 then 5x 1 = 5 ?
W video
At 27:27 I had worked out the same way, but I don't get how (5x-4) becomes (4-5x).
@williambailey9343
5 ай бұрын
Neither do I. Any explanation?
@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
4 ай бұрын
@@williambailey9343he swapped 2x + 3 to 3 + 2x as well even though it doesn’t matter
@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.
17:00
23:13
How can 5x-4 be written as 4-5x 27:20
@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
Where’s r cos alpha vid
Gosh this chapter is annoying, your explanation helped tho, thanks man
Never skip steps. It’s a bad habit to get into and loses marks in exams…
@roxc453
Жыл бұрын
I rlly need to remember this but I keep thinking the examiner can read my mind or something
@courtneylust
Жыл бұрын
@@roxc453 lol same
Endless pain and suffering I am tired
If this is a level maths me is whole alphabet 😂
3;30 mins in and no obviously
I'm so cooked
roasted
tired
Thank you
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?
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?