Super Hexagon for Trigonometric Identities | Trigonometry | Infinity Learn 

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Whoever made this hexagon deserves a Nobel prize.

I am 73 years old and recall how I struggled to memorise formulae when I was a student. I wish I would have had this tool back then. Terrific.

I am a grandmother brushing up on trig so I can help my grandchildren with this. It was so easy. Thank you!

5 years of engineering and no one mentioned that a hexagon could solve all my problems

This saved me From hitting my head against wall.

who else is getting better education here in YT rather than school only me?

I came here initially when I was in class 10 but now I am pursuing masters at IIT and I still find myself here again! Old memories!

I watched this video when trigno was first introduced to us in class 9th. I am in class 12th now and I just came back to this video to tell you guys that this is probably the most useful video I have ever watched on the internet. The hexagon trick has helped me multiple times over the last 3 years. Thank you❤️

This is the best learning channel i've ever seen.

I love the irony in naming the channel "Don't memorise".

It deserves to be called” super hexagon “ + it was such a wonderful presentation Thank you guys 💗

You just have to memorize this one formula! ~Don't memorize (2015)

Me: uses this technique in exams Teacher: Wait that's illegal!

"and there's more!" not the sort of thing we like to hear when we're studying maths!

every time she says “tan” rather than “tangent” i’m crying

Advice: Learn all the formulas and also keep this method in your mind. In case you get confused or forgot or while re-checking the exam paper use this method to do these. Because you cannot trust your brain especially in the examination hall where there is an atmosphere of fear and nervousness. So mark my words and Best of Luck for your career!! And Don't Memorize I love your videos. In the above advice I am not criticising but sharing my experience and ideas. The method you provided is just 🔥🔥!

After she drew the diagonal lines, uI just realized this is a great way to draw a transparent cube.

Me watching this before term one exam and mind blown that it can be so easy. Best channel 😉

First time a hexagon made me cry 😭😭😭😂😂 thank you

Trigonometry: "How many formulae do you want?" Super-Hex: Yes

The ones who have disliked might have probably studied all the trignometric formula without this method...

Okayy!!! So it's not only me who's suffering with trignometry....there are 24 lakh people with me!!! Wahh😂😂🔥🔥

Just amazing ! No words to express my thank to the person who made this video. Thank you so much. You should advertise this video so that a maximum number of students can get benefit from it.

🎓🎓🧩Mathematics formulas🧩🎯🎯 1. (α+в)²= α²+2αв+в² 2. (α+в)²= (α-в)²+4αв 3. (α-в)²= α²-2αв+в² 4. (α-в)²= (α+в)²-4αв 5. α² + в²= (α+в)² - 2αв. 6. α² + в²= (α-в)² + 2αв. 7. α²-в² =(α + в)(α - в) 8. 2(α² + в²) = (α+ в)² + (α - в)² 9. 4αв = (α + в)² -(α-в)² 10. αв =1. (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α) 12. (α + в)³ = α³ + 3α²в + 3αв² + в³ 13. (α + в)³ = α³ + в³ + 3αв(α + в) 14. (α-в)³=α³-3α²в+3αв²-в³ 15. α³ + в³ = (α + в) (α² -αв + в²) 16. α³ + в³ = (α+ в)³ -3αв(α+ в) 17. α³ -в³ = (α -в) (α² + αв + в²) 18. α³ -в³ = (α-в)³ + 3αв(α-в) ѕιη0° =0 ѕιη30° = 1/2 ѕιη45° = 1/√2 ѕιη60° = √3/2 ѕιη90° = 1 ¢σѕ ιѕ σρρσѕιтє σƒ ѕιη тαη0° = 0 тαη30° = 1/√3 тαη45° = 1 тαη60° = √3 тαη90° = ∞ ¢σт ιѕ σρρσѕιтє σƒ тαη ѕє¢0° = 1 ѕє¢30° = 2/√3 ѕє¢45° = √2 ѕє¢60° = 2 ѕє¢90° = ∞ ¢σѕє¢ ιѕ σρρσѕιтє σƒ ѕє¢ 2ѕιηα¢σѕв=ѕιη(α+в)+ѕιη(α-в) 2¢σѕαѕιηв=ѕιη(α+в)-ѕιη(α-в) 2¢σѕα¢σѕв=¢σѕ(α+в)+¢σѕ(α-в) 2ѕιηαѕιηв=¢σѕ(α-в)-¢σѕ(α+в) ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв. » ¢σѕ(α+в)=¢σѕα ¢σѕв - ѕιηα ѕιηв. » ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв. » ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв. » тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв) » тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв) » ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв) » ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα) » ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв. » ¢σѕ(α+в)=¢σѕα ¢σѕв +ѕιηα ѕιηв. » ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв. » ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв. » тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв) » тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв) » ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв) » ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα) α/ѕιηα = в/ѕιηв = ¢/ѕιη¢ = 2я » α = в ¢σѕ¢ + ¢ ¢σѕв » в = α ¢σѕ¢ + ¢ ¢σѕα » ¢ = α ¢σѕв + в ¢σѕα » ¢σѕα = (в² + ¢²− α²) / 2в¢ » ¢σѕв = (¢² + α²− в²) / 2¢α » ¢σѕ¢ = (α² + в²− ¢²) / 2¢α » Δ = αв¢/4я » ѕιηΘ = 0 тнєη,Θ = ηΠ » ѕιηΘ = 1 тнєη,Θ = (4η + 1)Π/2 » ѕιηΘ =−1 тнєη,Θ = (4η− 1)Π/2 » ѕιηΘ = ѕιηα тнєη,Θ = ηΠ (−1)^ηα 1. ѕιη2α = 2ѕιηα¢σѕα 2. ¢σѕ2α = ¢σѕ²α − ѕιη²α 3. ¢σѕ2α = 2¢σѕ²α − 1 4. ¢σѕ2α = 1 − ѕιη²α 5. 2ѕιη²α = 1 − ¢σѕ2α 6. 1 + ѕιη2α = (ѕιηα + ¢σѕα)² 7. 1 − ѕιη2α = (ѕιηα − ¢σѕα)² 8. тαη2α = 2тαηα / (1 − тαη²α) 9. ѕιη2α = 2тαηα / (1 + тαη²α) 10. ¢σѕ2α = (1 − тαη²α) / (1 + тαη²α) 11. 4ѕιη³α = 3ѕιηα − ѕιη3α 12. 4¢σѕ³α = 3¢σѕα + ¢σѕ3α » ѕιη²Θ+¢σѕ²Θ=1 » ѕє¢²Θ-тαη²Θ=1 » ¢σѕє¢²Θ-¢σт²Θ=1 » ѕιηΘ=1/¢σѕє¢Θ » ¢σѕє¢Θ=1/ѕιηΘ » ¢σѕΘ=1/ѕє¢Θ » ѕє¢Θ=1/¢σѕΘ » тαηΘ=1/¢σтΘ » ¢σтΘ=1/тαηΘ » тαηΘ=ѕιηΘ/¢σѕΘ

If only I had discovered this channel 2 years ago😞

you saved me so much studying and memorization

7 year ago video No other video on yt can beat this video to learn trigonometry formule🔥🔥🔥🔥🔥🔥🔥🔥

I am a teacher of mathematics, I like your simplicity. As a matter of facts you are using less word and figures to explain more.

i actually love this video. not only is the mnemonic extremely useful, but the repetition is great.

A wise math professor once told me "There's no such thing as a free lunch. Where you get *blank*, you lose *blank*". In this case, you get a tool that holds so many formulas in a nice little package, but you lose the understanding behind those formulas which can already make them feel like common sense in the first place. For example, the equation: sin^2(x) + cos^2(x) = 1 should be obvious when you think about it. It's essentially Pythagoras' Theorem applied to the unit circle. With a little algebra, you can divide each term on both sides by cos^2(x), and derive the equation: tan^2(x) + 1 = sec^2(x) I can continue, but my point is that knowing a formula is okay for a test in high school, but you won't get far beyond that using this hexagon alone. Take some time to actually learn and understand where these formulae come from in the first place, and it should hopefully click without trying to memorize it.

YOU CAN USE THIS WITH DERIVATIVES! Though its a bit difficult to see, there are some noticeable patterns. Once i noticed these, I haven’t had trouble with these derivatives at all! You’re not gonna understand without writing it out. Its a bit complicated at first glance, but simple when you understand it. I just drew the hexagon (without the edges, only the lines in between. It looks like a x with a horizontal line) 1. Search up the trig derivative online. Write them down across a page. 2.Then under each function, draw the hexagon thing 3. trace a line from the trig to derivative using a different color pen. Do you notice the patterns? Take a moment to study it for yourself. Anyway, hopefully you understand this: I found these patterns: Obtuse angles create fractional derivatives, Accute angles create singular or multiplication derivatives Following the inner lines left into the center and out, will give negative derivatives. Following the inner lines right into the center and out, will give positive derivatives. Csc and sec repeat themselves in their derivatives. The derivative angles on the left are opposite of those on the right. Ex: following the inner lines, draw a line from tan to it’s derivative 1/cosx. The line went right in a obtuse angle, so it’s solution is a positive fractional derivative. Ex2: following the inner lines, draw a line from cot to it’s derivative -1/sinx The line went left in a obtuse angle, so it’s solution is a negative fractional derivative. The angle is opposite to tangent. Ex3: following the inner lines, draw a line from sin to it’s derivative: cosx. The line went right in a acute angle so the solution is a positive singular or multiplication derivative. Ex4: following the inner lines, draw a line from cosx to its derivative -sinx The line went left in a acute angle, so the solution is a singular or multiplication derivative. The angle is opposite to sinx. Ex5: draw a line from secx to to tanx (not the derivative) The line goes right first, and is a acute angle, so the derivative is positive multiplication. Since it is sec, it’s repeated. So, the derivative is Secxtanx. Ex6: draw a line from csc to cot (not it’s derivative) The line goes left first so the derivative is negative multiplication. Since its csc, it is is repeated. So the derivative is cscxcotx. Haha, I did not explain that very well, so I encourage you to try figuring this out yourself! The pattern could probably be simplified a bit. For instance, it’s better to say the top accute angles are singular while the bottom accute angles multiply something by themselves. But whatevs! I wish you the best of luck!

I cant explain how this video helped me! It literally saved my lots of time. I drew this hexagon in my exam hall and just solved things so easily. And the way the presenter presented was just top notch.💫

I think they need to introduce this in schools. It's really good

Looks like I am the only one who discovered this channel on time (Edit:Whoaaaa... Thanks for the likes!!!!!!!)

Hello dear teacher I am from Pakistan and want to say that this super hexagon formula very much help me to understand my trigonometric identies really its amazing method..👍👍👌❤👌

This person should get an award.... For inventing thiss....

During this pandemic we are learning trigonometry and on every Saturday there is an activity. Our teacher told about this in activity period and I think that he had taken idea from this only . Thank u so much for discovering this ... Othrwise our teacher would have suggest it to learn only

If at all some one explained me like this 54 years ago I never have failed and afraid of trigonometry. I SALUTE THOUSANDS TIMES.

This has made it easier for me to master all the trig functions. This is the best summary of the trig functions

This shouldn't be underrated ✨thank you ma'am thank you very much

Where was this wonderful lecture hidden??? 😍

Brilliant stuff , I was desperately searching for a trick .

Actually trignometry is hard for me but after watching this video it become more intresting and easy to learn. thankyou infinity learns

I would be the happiest person in the world if I saw this hexagon in my school days😭....u made 50%trig in one single hexagon bro awesome.....

If you'll see clearly you'll find a 3D cuboid in hexagon with diagonals.. see carefully

I've got to show this to my teachers!!

Best line- "wait there is more "

we just started our trigonometry unit this week. had i not known about this super hexagon, i’d probably be crying myself to sleep every night. thank you so much for sharing this resource.

This is superb. I love this mnemonic.

Trigonometry:I'm toughest field of maths to master. Super- Hexagon: I'm about to end this man's whole Career.

Your a genius ✨✨✨✨🙇🏻‍♀️ thankyou soooo much

BRILLIANT and life saving vedio

This is the only learning channel I actually subscribed to.

Guys if U didn't waste time on this then just by practice U can learn basic ones and derive others easy pizzy but I respect their innovation and it does not cover the complex formulas like 2thieta 3 thieta...and gp angles ap angles

look at the 3rd letter of coT, coSec, seC coT = 1/Tan coSec = 1/Sin seC = 1/Cos 3:20 this is a good use for trig equations tho sometimes u'll need to prove for proof Q's by writing out e.g.// cot = cosec/sec = 1/sin */* 1/cos still a helpful quick hand if u rmb for non proof Q's 2:50 6:55 7:50 9:30 10:20 11:20 ! identities to memorise 12:10 anticlockwise (or u can just rearrange from clockwise) 13:10 understanding where it's derived from is still important, but this is an add-on to help

This type of education cannot be thought in our schools. Amazing video for remembering formulae

There's about 5 minutes of content in here, the rest is just repetition

One hexagon to rule them all

Thankkk youuuuu so muchhh yaar❣️ It's very easy and quick to learn TYSM

thanks a lot ! U guyz are one of the only reasons i understand trigonometry at all ! Fricking love u guyz :)

This was the most and best helpful method to learn trignometry! Thank you so much guys , it's very useful!

The most interesting thing is to remember the Logic with full concentration and Serousness. And thats it Everything is Upto you.

Thank you so much, i always struggling with trigonometric, this hexagon is a life saver. If only i discovered this fantastic channel sooner.

I am really confused on how people are founding this to be helpful The procedures give in this video are soo complicated that it would be better to just to memorize And if you dont want to memorize these formulas then you can think of these ratios in context of sides of triangle Like,If you want to find out: CotA x SinA = ? Then,CotA = 1/TanA CotA = B/P SinA = P/H P cancels out on multipling these ratios give B/H which is equal to CosA This can be done even thinking these ratios in terms of sin and cos(this is easier), whatever suits you For the trigonometric identities just divide the Pythagoras theorem by P2,B2 and H2 you will get all the identities. I think all you need to memorize for understanding basic trigo is just SinA = P/H = 1/CosecA CosA = B/H = 1/SecA And TanA = P/B or SinA/CosA = 1/CotA This ofcourse will need some practice

Amazing. If I knew this tips before, my life would be easier.

I have been struggling with this so much, I even missed my test to have an extra day to study, I take it tomorrow and my friend got a 55 on it. This seriously helps and I honestly feel so much better about taking the test.

I will recommend your channel to my friends. Thank you for this wonderful video!

After 7 years also it is more important and too helpful 🤗🤗 Thx👏 And know that I subscribed 👍

Is it OK if i memorise this video? It's sooo awesome btw.

The whole concept of trigonometry is covered by using a super hexagon really great

Thank you so much 🙏🙏 This is really helpful and I am going to share it with others.

Thank you mam , through this i have learned half of trigonometry🎉😊

It's really a vary helpful video...thanks for this type of video ... it's really interesting to study all formulas of trigonometry with a hexagon...

These formulae were the basic ones. Difficult formulae are of compound angles and conversations from product to sum and vice versa.

This really helped me tomorrow is my exam and i am always confused remembering identities but this video really helped me i understood very well Thank you so much ❤️

i was always searching a channel which teaches in English it was hard to find but I found the best one here

I just find this video before my exam (my exam is tommorow) 😀😁😇🤗😐😍😍

This is the best trigonometry video on the earth.. thank you so much ma'am.. I'm so obliged🙏

A very big thanks to the the creator of this Super Hexagon...What an amazing explanation done by 'Don't Memorise'!!!

Thank you! I needed this for my maths exam today. This saved my life

I Discovered this channel on perefect time just before my exams. Thank u very much

Cool! I will show this to my students this year. Thanks for posting!

*¡this would had helped me a lot during my Fall 1989 trigonometry course taught by Donald F. Mazukelli (1934 - 2000 at 66 years old due to cancer) at Los Angeles Valley College "Home of The Monarchs" [Lions and Lionesses]!* 3:23 am Pacific Daylight Savings Time on Tuesday, 5 October 2021 Common Era or CE formerly known as Ano Domini or AD

I am literally in love with this channel it's amazing ,it has solve my alot of problems and it's to easy to learn now ... ♥️♥️♥️♥️ Thank you

Wow this is mind-blowing! Even if you understand and learn you won't be able to recall the formulas this easily. Good job Don't Memorise team.

Woah this blows my mind🤯♥️ It's so simply explained here, which teachers in my school failed to do 😑.

Just wow 😍

These are really basic formulas you don't even need to memorize them. It would make more sense if make tricks on trigonometric functions and inverse trigonometric functions formulas because their are around 50 formulas.

RU-vid randomly put this in my recommendations. Is there another hexagon for all the inverse functions?

How can someone dislike such a helpful video?

i understand this better, thank you so much!!

Amazing you have done it beautifully and clearly. ❤️❤️❤️❤️❤️❤️❤️👍

By practing, I have learnt all this identities.👍🏻 Therefore use this super hexagon and keep practicing 💓 so that you will able to do all trigonometry without any help.✍🏻

Hello guys! I'm a 58 years old mathematician wanna be all my life. I just found your channel and I am petrified. Well you have another student on the way! Thank you so much!

This was so helpful! Thank you 🥹

I am glad that I have found this video or else I have to stay up all night just memorizing the formulae and getting tensed about my test tomorrow.

OMG!!! I could get more marks in math in my 10th and 12th exam if I knew this... Trigonometry was nightmare for me...

1 Million likes is not enough for this video.

Thank you.... For your wonderful teaching ❤