Trig Visualized: One Diagram to Rule them All (six trig functions in one diagram)

Рет қаралды 315,060

10 ай бұрын

In this video, we show a single diagram consisting of various triangles that connects the six primary trig functions (sine, cosine, tangent, secant, cosecant, and cotangent) to lengths of line segments created from the unit circle (circle of radius 1). We use the diagram to explain features about why tangent and secant aren't defined at pi/2, the possible outputs of these six functions, and the Pythagorean trig identities. We also briefly discuss the fact that the "co" on three of the functions refer to the "complementary angle."
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
This animation is based on a classic diagram for describing the six main trig functions. If you want to know more trig identities, check out my playlist:
• Trigonometry
or check out this Wikipedia article:
en.wikipedia.org/wiki/List_of...
Here is an interactive version from Tien Chih using Desmos:
www.desmos.com/calculator/26f...
Here are alternate videos with the same diagram:
• All 6 Trig Functions o...
• Visualization of trigo...
#math #mathvideo #math #trigonometry #trigidentities #identity #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #circle #pythagoreantheorem #obtuseangle #acuteangle #angle #sine #cosine #tangent #secant #cosecant #cotangent #learnmaths
To learn more about animating with manim, check out:
manim.community
_______________
Music in this video:
Meditation Impromptu 02 by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/...
Source: incompetech.com/music/royalty-...
Artist: incompetech.com/

Пікірлер: 528

@RandyKing314 9 ай бұрын

i’ve never seen this diagram…even a static version is quite informative, but the animation knocks it out the park…thanks!

@MathVisualProofs 9 ай бұрын

👍😀

@bart2019 9 ай бұрын

The static version would have been clearer still if the angle was not so close to 45°, so that the sine and cosine are virtually the same value.

@MathVisualProofs 9 ай бұрын

@@bart2019 yes. Hard to make space for everything. But the angle is not 45 :)

@Mark73 9 ай бұрын

I've seen it before in a math encyclopedia (but never an actual textbook) but seeing it animated like this is far better.

@MathVisualProofs 9 ай бұрын

@@Mark73 😀👍

@clairecelestin8437 9 ай бұрын

This diagram is basically a full semester of trig, and if you remember it you can derive most of the knowledge of trigonometry. For students, please remember that there is also a skill of trigonometry, which comes from repeatedly applying the knowledge. In particular, a lot of trig problems are only solvable if you recognize the different trig identities and use them to convert the form of an equation into something you can deal with. It's worthwhile to put in the practice so you can recognize these patterns.

@tiskbubbles4688 7 ай бұрын

For a full coverage you should also see a visual proof of the Pythagorean theorem, a derivation of the special angle values, and the proof of the angle sum identities (the rest of the identites follow from these and the Pythagorean ones algebraically). A higher level overview can mention their power series definitions (which generalize to nonreal inputs, like complex numbers or matrices, and are considered the formal definitions of the functions) and also Euler's formula.

@tiskbubbles4688 7 ай бұрын

Law of sines and cosines is also good to prove, although it's more a fact about triangles than just the trigonometric functions themselves.

@deltalima6703 5 ай бұрын

Trig identities turn math into magic at higher levels. I am no shin lim, lets just say.

@jamesralston5293 2 ай бұрын

So many people are scared of this , what a waste

@kurchak Ай бұрын

Thank you, this motivated me to keep doing practice problems. I understand trig pretty decently, but I realized after even a week or two not using it I lose it all. But it really is a use it or lose it sort of math.

@shreeniwaz 9 ай бұрын

I learnt trigonometry since highschool.. WHY DIDN'T THEY TEACH THIS EVER!? It's so easy and sensible in this way.. why!!??

@hmmmidkkk 6 ай бұрын

Because they themselves don't understand the concept that's why they're teaching and not in a higher paying job

@shreeniwaz 6 ай бұрын

@@hmmmidkkk Isn't this a tragedy in a way? If you're meritorious you'd rather want to land up on a high paying job while teaching is considered a low profile career.. actually teaching is the most sensitive profession in social POV

@ahnaf1158 5 ай бұрын

@@shreeniwaz kulukulu is the reason

@SirGryflet 3 ай бұрын

@@hmmmidkkk I would be wary of painting all teachers with the same brush. Ludwig Wittgenstein was a teacher, and Bertrand Russell was a lecturer.

@CrusaderGeneral Ай бұрын

they were honing their skills to teach gender studies and critical race theory

@Alnakera 9 ай бұрын

I remember clearly back in highschool asking my teacher "what does the tan represent on the unit circle?" He said, it's just the ratio of sin and cos. Ever since then anything other than sin and cos were just equations and had no graphical meaning. +10 years later, I finally got a legitimate answer. Thanks!

@MathVisualProofs 9 ай бұрын

Glad to help!

@hacker64xfn99 9 ай бұрын

How sad this must have felt, I remember when our high-school professor showed as what the tan look like on the trigonometric circle, we did not even know what is 'sec' so we could apply the pytha theorem (back then) lol

@perrymaskell3508 9 ай бұрын

Suddenly the complimentary functions and the identities make so much sense. Brilliant way of showing all the trig functions.

@MathVisualProofs 9 ай бұрын

👍😀

@owen7185 4 ай бұрын

💯💯💯💯

@SpencerWilliamsIV 9 ай бұрын

Jesus, no one has ever explained to me why that darn function is called tangent. Thank you.

@kurchak Ай бұрын

Yeah that was a huge eye opener wasn't it lol. Anyone who thinks they are "bad" at trig was probably just taught by someone who had no clue how to properly teach trig. I'm going to watch this video every morning when I wake up from now on lol

@jmscnny 9 ай бұрын

Holy crap. It has only taken me 60 years to stumble across this explanation.

@MathVisualProofs 9 ай бұрын

Better late than never. :)

@Thrakerzog 4 ай бұрын

You are by far a better teacher than ANY of the teachers at my old high school. In just over 4 minutes, you explained in a clear concise way the fundamentals of trigonometry. Thank you!

@MathVisualProofs 4 ай бұрын

Thanks for the kind words. Glad this helped.

@paulfrost8952 9 ай бұрын

I have a reasonable ability in mathematics. However to find out at the age of 61 that the co in cosine etc means complimentary is a revelation. I am somewhat surprised that that was never mentioned to me all those years ago “hay ho”. So just for that thank you very much.

@MathVisualProofs 9 ай бұрын

😀👍

@jasonrubik 7 ай бұрын

my complements to you sir

@garrettbates2639 6 ай бұрын

I took trig in university, and understood it pretty well at the time. And I've seen the static version of this diagram, but it never really made sense to me because these functions were never taught to me this way, outside of sine and cosine. This explanation was really cool and makes a ton of sense.

@MathVisualProofs 6 ай бұрын

Glad you liked it!

@markdonnelly1913 9 ай бұрын

Imagine if every school took these functions to the simple basic level you just did in only a couple of minutes. There would be nothing scary about trig again. I wish it had all been expained so easily when I was at school. It took me to research it myself years later to understand trig. Great video.

@markdonnelly1913 9 ай бұрын

I also just subscribed to your channel. I Was looking for proofs in video form of the sin and cosine rules for non right triangles. Do you have one, or could you make one ?

@MathVisualProofs 9 ай бұрын

Can you specify which rules you mean? I do have a trig playlist, but I can take requests and see what I can do.

@markdonnelly1913 9 ай бұрын

@@MathVisualProofs the sin rule ... a/sinA = b/sinB=c/sin C ... the cos rule ... a2=b2+c2-2bcCosA, or cosA=(b2+c2-a2)/2bc. I can't superscript the squares for a, b and c in the equation sorry. We were told the formula at school, but not the proofs. I always wanted to know the whys as well as the whats

@MathVisualProofs 9 ай бұрын

@@markdonnelly1913 here’s law of cosines : Law Of Cosines II (visual proof) kzfaq.info/get/bejne/hK6ofZaLxJucfKs.html (I have another too). Don’t have law of sines yet.

@christophercharles9645 9 ай бұрын

THAT'S what all those buttons I never use on my calculator are...thank you!

@willie333b 9 ай бұрын

The diagram is really intuitive

@RecOgMission 9 ай бұрын

From a nerd and someone with a decent level of maths education: This is brilliant! It makes so much sense out of these concepts, all in one connected image!

@MathVisualProofs 9 ай бұрын

👍😀

3 ай бұрын

heh

@QuantumAstrophile 9 ай бұрын

Incredibly helpful. It bridged geometry into trig for me. Trig makes so much sense now.

@MathVisualProofs 9 ай бұрын

Glad it helped!

@randydewees7338 9 ай бұрын

LOL. I remember hitting the windshield in my 2nd Calculus class when I was suddenly confronted with the reality that I had either never learned the trig identities or had completely forgotten them. The prof was truly bad too, so instead of scrambling I decided to drop that class, review some basic math, and burned through the class the next semester. This vid might have saved the day, but this all happened in 1982.

@mmeis2389 9 ай бұрын

As a mechanical draftsman in the 70/80s descriptive geometry using drawings technical methods was used similiar, but not knowing trig hurt my career. I had to relearn it starting with ratios...do they even teach this anymore. Oscar Had A heap Of Apples saved my butt. sin = O/H cos=A/H tan=O/A and of course pythagoreus....A2+B2=C2 Your diagram just opened my eyes - and brought it all together. Very good Sir. KISS as we would say in designing: Keep it simple stupid. Thank you.

@MathVisualProofs 9 ай бұрын

👍

@robelbelay4065 2 ай бұрын

Mind Blown! First time grasping why these things are the case instead of pure memorization

@sheepcommander_ 9 ай бұрын

thank you for gifting me this after I just started precalc

@mplgraphicxindia1558 12 күн бұрын

The fact that he explained it so calmy i felt like watching a discovery channel's documentary about an animal called trigonometry in the forest of mathematics and this guy is explaining the ferocious animal trigonometry would react when it faces its different types of prey and the prey are the different angle measures

@teacher_of_the_arcane5399 9 ай бұрын

Just remembering the agony of putting all that information into my usable knowledge !! Then remembering trying to teach that same info to my students for twenty years !! Saving and Sharing this. Blessings for the individual who put this together !

@MathVisualProofs 9 ай бұрын

Thanks!

@randomyoutuber4829 27 күн бұрын

MVP: gives a detailed explanation about trigonometry and equations Me: "Mmm, yes. Circle is made from triangles, which make more triangles"

@pinedelgado4743 9 ай бұрын

This is one of the BEST math videos I've ever seen!! THANK YOU!! THANK YOU!! THANK YOU!!

@MathVisualProofs 9 ай бұрын

Glad it was helpful!

@karthikbhat93 4 күн бұрын

Wow! Mind Blown🔥. Why doesn't this diagram still not available in 🇮🇳 text books. Is this the best video ever on maths??

@MathVisualProofs 4 күн бұрын

Thanks! 😎

@bharat7917 9 ай бұрын

I wish I was taught trigonometry like this..

@alphalunamare 9 ай бұрын

I must admit to having to watch this slowly and think through the 'what is obvious' bits but I get it. I think it's brilliant! :-) I love the naming of 'tan' it is so obvious from the diagram. It is reminiscent of that tablet found on the beach after that massive volcanic eruption on the island of Sohcahtoa.

@MathVisualProofs 9 ай бұрын

Glad you liked it.

@MrSilversMathSheets 10 ай бұрын

This is really nice. You should do one on the double angle theorems for sin and cos. There is a nice one that looks just like your Diophantus diagram from a few months ago.

@MathVisualProofs 9 ай бұрын

Yes! I have a couple planned/in the works. Slowly but surely I'll get around to them I think.

@tomboytomgirl5356 6 ай бұрын

This is the absolutely most brilliant visual presentation of trigonometry that I've ever seen. I've seen many, many. I nominate you for the Trigonometry Nobel Prize! 😎😎😎😎

@kennithlambert2563 9 ай бұрын

Your diagram really helped me with the infinity values by explaining it in simple terms like y and x never cross. I've seen the same diagram in motion but slowing it down I was able to grasp more.

@MathVisualProofs 9 ай бұрын

Excellent!

@preethalal81 8 ай бұрын

Best explanation ever

@user-mf7li2eb1o Күн бұрын

OKAY WOW SO MUCH INFO COMPRESSED INTO 4 MINS

@MathVisualProofs Күн бұрын

Longer version on my channel isn’t so compressed :)

@SantoshKumar-pz4qu 2 ай бұрын

This is lit, Noone in highschool / tuitions, ever explained like this to me. I wonder why they missed such simple stufff and keep the kids, breaking their head. Many thanks for sharing!!

@MathVisualProofs 2 ай бұрын

Glad it was helpful!

@user-ks3ol3lw3b Ай бұрын

When I had algebra and geometry in high school, I always sat there thinking 'but what is the point?' THIS explains the point of trig functions in a way I never saw. I'd have to go back through it one at a time to get them all, but at least I see the logic now.

@ezrad5273 9 ай бұрын

I went to high school in SoCal and all we learned from geometry is the mnemonics for the trig functions: SACAGAWEA which was based on some female Indian name. I wish I had you as teacher.

@audreymarsh1827 9 ай бұрын

Do you mean SOH CAH TOA ?

@raulsantinolopezrodriguez8349 6 ай бұрын

Gracias por la Gran explicación. La proyección de la tangente fuera de la circunferencia, me dió otra perspectiva de las funciones.

@owen7185 4 ай бұрын

Basically a whole chapter of trig is summed up beautifully by this diagram and its labels

@MathVisualProofs 4 ай бұрын

Glad it helps supplement the text!

@petra_cheung 6 ай бұрын

What a neat and to-the-point representation! Thank you so much!

@MathVisualProofs 6 ай бұрын

Thanks for checking it out!

@PsychologyNutshelled Ай бұрын

this is by far one of the most important thing that I've learnt on you tube

@MathVisualProofs Ай бұрын

😀

@eternng5706 Ай бұрын

Thanks for sharing this information. It really helped me to understand trigonometry better. Hope you can create more videos like this

@owen7185 4 ай бұрын

Best trig description ever made

@przemysawkwiatkowski2674 9 ай бұрын

Finally! "Co-" makes sense! 😁

@MathVisualProofs 9 ай бұрын

👍😀

@caststagemysteries 3 ай бұрын

Keep the ideas in your head; excellent technique.

@vandinem 8 ай бұрын

This is a very creative explanation, and the animation brings it to life. Well done!

@MathVisualProofs 8 ай бұрын

Thank you very much!

@fsmendesable 6 ай бұрын

Thank you and greetings from Brazil!

@MathVisualProofs 6 ай бұрын

👍

@mohit1768 2 ай бұрын

Thanks a lot 🙏 Surely gonna help a lot in mechanics.

@richardsttati317 8 ай бұрын

Woooow I have an impermeable brain , but this video finally made it porous! Thanks 🙏

@arandomguy9669 2 ай бұрын

I know school messed up when this 4 minute video made me grasp trigonometry when years of textbook problems couldn't.

@jamespaul4618 9 ай бұрын

Awesome. . This video is enlightening. In the past I struggled to understand the various relationships. This VISUALZATION is so powerful.. Thanks for sharing your insights. regards / djb.

@MathVisualProofs 9 ай бұрын

Glad it was helpful! Thanks for checking it out.

@bouazabachir4286 6 ай бұрын

Thanks a lot professor I follow you from Algeria

@MathVisualProofs 6 ай бұрын

Glad to have you here!

@jashouse9003 2 ай бұрын

I Understand trigonometry now! Thanks

@lodgechant 17 күн бұрын

WONDERFUL! Thank you so much!

@MathVisualProofs 17 күн бұрын

Thanks for watching!

@curiousaboutscience 9 ай бұрын

These are definitely great!

@MathVisualProofs 9 ай бұрын

Thanks! 👍

@eaterofcrayons7991 3 ай бұрын

I was unable to visualize all of the non hyperbolic tangent functions before this video. Great stuff!

@MathVisualProofs 3 ай бұрын

Glad this helped!

@javiermancheno8531 7 ай бұрын

Just BRILLIANT knowledge and imagination as well ! Many thanks for sharing , okay ?

@MathVisualProofs 7 ай бұрын

Thank you!

@RandyKing314 7 ай бұрын

good thing i’m doing a trig function unit with my alg 3 class. i will refer my students to this vid during our transition from the geo ratios to the functions. thanks again!

@MathVisualProofs 7 ай бұрын

Glad it can help!

@MattH-wg7ou 6 ай бұрын

Dude. Very well done. This static diagram as a poster should be standard trig classroom accessories!

@MathVisualProofs 6 ай бұрын

Agree. I wonder if it exists…

@Heyboi155 3 ай бұрын

AMAZING CONCEPT VISUALISATION THROUGHT THE. STATIC DIAGRAM AND FUNCTION👍

@MathVisualProofs 3 ай бұрын

👍😎

@romanieo 9 ай бұрын

Dude, you're doing the "good Lord's work"!!! Wow. This is one of the most important vids on KZfaq.

@MathVisualProofs 9 ай бұрын

Appreciate this comment!

@VladimirDjokic 6 ай бұрын

The best trig diagram. Thanks ❤

@MathVisualProofs 6 ай бұрын

👍😀

@Dan14833 6 ай бұрын

That was so helpful. Thank you

@MathVisualProofs 6 ай бұрын

Glad it helped!

@sang81 9 ай бұрын

If we assume any other radius lets say r then just multiply each identity with r to het the complete picture. Also there are two interpretations of tan, cot, sec, csc like there are two interpretations for sin amd cosine (check the diagram for two parallel vertical lines amd horizontal lines which are sin and cos. Plus when angle is 45 sin =cos , tan = cot and sec = csc. Verify from the diagram. I have a beautiful diagram on my whiteboard 😊

@querrythis Ай бұрын

Man, I never understood what an identity meant. Just memorized it and solved the problem without knowing what rhe heck I was solving.

@DesandSam 9 ай бұрын

Some Officers Have Coaches And Horses To Order Around Sin = Opposite/Hypotenuse Cos = Adjacent/Hypotenuse Tan = Opposite/Adjacent That's how I was told to remember it at school. I'm 59.

@Jechew 7 ай бұрын

Beautiful video!

@MathVisualProofs 7 ай бұрын

Thank you very much!

@brandonfox9618 9 ай бұрын

For cot(θ), you can also use the idea of alternate interior angles being congruent to help you along the way!

@MathVisualProofs 9 ай бұрын

Nice!

@brandonfox9618 9 ай бұрын

@@MathVisualProofs Thanks! I do have a BS degree in math, btw!

@AsifAslam-vf7ne 4 ай бұрын

I can thank you enough, Thank you so much 🎉❤

@technicallittlemaster8793 9 ай бұрын

Weirdly enough, I don't know if I should acknowledge this but this diagram was explained in the byjus class 10 science videos back in 2017. Those days they were really good.

@MFarhanAkterArnab 10 ай бұрын

Another one might be: csc^2(theta) + sec^2(theta) = {cot(theta) + tan(theta)}^2

@nicki8731 10 ай бұрын

sin2α = 2sinα * cosα cos2α = cos^2(α) - sinα^2(α) tan2α = 2tanα / 1-tan^2(α)

@MathVisualProofs 10 ай бұрын

A nonstandard one for sure.

@MathVisualProofs 10 ай бұрын

Not sure I see these directly here.

@rdeseslimakale 9 ай бұрын

also 1 + tan^2 = sec^2 and 1 + cot^2 = csc^2 then 2.tan.cot = 2 so tan.cot = 1 therefore 0.infinity = 1 )

@judelarkin2883 9 ай бұрын

Nicely done.

@MathVisualProofs 9 ай бұрын

Thank you!

@coachhannah2403 Ай бұрын

That was how I learned trig in 1972-3!

@davidplanet3919 6 ай бұрын

It’s good to move the point to the other quadrants to see what happens to the functions. You can also prove double angle identities using the unit circle.

@LittlePaimon 10 ай бұрын

nice job！

@MathVisualProofs 10 ай бұрын

Thanks!

@obnoxioussubconscious6649 9 ай бұрын

Now I finally know why they are called the Tangent and Cotangents , They ARE Literally what they are called

@MathVisualProofs 9 ай бұрын

👍

@Adhithya2003 9 ай бұрын

Salute to your efforts good sir.

@MathVisualProofs 9 ай бұрын

Thanks!

@budgarner3522 9 ай бұрын

Great job MVP. This diagram ought to be in every geometry and trig book in America but isn't. Add: 1) automated, 2) static and 3) math experiment as a hands-on exercise to prove it to the student. Today, there is "not enough time" or "it's not in the curriculum, scope and sequence or district mandates". This with the unit circle at the key radian measurements (pi, pi/2, pi/3, etc) are the visual presentations to allow the students to understand the definitions and abstract concepts of trig. History buffs, did the definitions of trig or the diagrams come first? (20+ year retire math teacher; 16 in geometry.)

@MathVisualProofs 9 ай бұрын

Thanks!

@guilhermecampos8313 2 ай бұрын

This is beautiful!

@MathVisualProofs 2 ай бұрын

😀👍

@MeathammerFour 2 ай бұрын

You’re doin the Lord’s work brother! Keep it up!

@MathVisualProofs 2 ай бұрын

Thanks!

@silentbubble 9 ай бұрын

Very nice! Could you make another video for the hyperbolic trig functions?

@MathVisualProofs 9 ай бұрын

I’ll see about that. It’s a good idea. Thanks!

@gabrieletrovato3939 4 ай бұрын

I just love this channel ✨✨✨

@MathVisualProofs 4 ай бұрын

Thanks!

@aktisfm 2 ай бұрын

one question from a high schooler who has a hard time doing math or taking concepts for granted until they feel like they understand it enough to have come up with it themselves (for whom this video has been an absolute lifesaver): how does SOH, CAH, TOA play into this? how/why does that work? i can see that in this diagram, sin(x) (gonna say that instead of theta) IS the measure of the side opposite to angle x, rather than "the opposite side over the hypotenuse". same with cos(x) (but respectively). at least TOA for tan(x) makes sense within this diagram!

@MathVisualProofs 2 ай бұрын

When you scale the circle to have radius r, the x and y coordinates become r*cos(t) and r*sin(t) and the triangle is similar to the original. So here you can take see that sin(t) is opposite over hypotenuse because the r’s cancel in numerator and denominator. Does that make sense?

@aktisfm 2 ай бұрын

@@MathVisualProofs that does make sense! and the circle here has r = 1 and doesn't need to be scaled, so you didn't show that cancellation, is that right?

@MathVisualProofs 2 ай бұрын

@@aktisfmthat’s right! The unit circle is used as nice circle because then the ratios work out as just sine and cosine. All circles are similar so you just need one to understand trig.

@AdrianCHOY 9 ай бұрын

Well done!

@MathVisualProofs 9 ай бұрын

Thanks!

@ciaucia156 6 ай бұрын

Excellent! Educational! A huge thank you! sec × sin = tan × 1 shines in my eyes pink × blue = yellow × white and this provoked me for a bit another look at secants... with memorable trigonometric "trinity" and "co-trinity" formulas :) tan = sec × sin cot = csc × cos need to say, that those are easier identifiable on "secant (ray) centric" drawing (lines x=1 and y=1 are plotted instead of tangent) which is an alternative to this, let's call it"tangent centric"

@MathVisualProofs 6 ай бұрын

👍😀

@PaloniemiJ 9 ай бұрын

This is a great viswualization tool. It would, hoiwever, bet easier to understand the triangle similarities in the initial setup if the angle shown were not so close to pi/4. :)

@MathVisualProofs 9 ай бұрын

Yes. I tried various angles and it was hard to read either sin or cos depending on the angle. So I went close to pi/4 (though not pi/4). Thanks!

@djdigital3806 7 ай бұрын

I finally understand Trigonometry!🤗 I’m an Electrical Engineering Technician. I dropped out of college because of Calculus. Now l understand.

@MathVisualProofs 7 ай бұрын

Glad this helped!

@kittybecker-smits154 5 ай бұрын

Awesome. Thank you. 🙌🎀

@MathVisualProofs 5 ай бұрын

No problem 😊

@exameye944 5 ай бұрын

Awesome information

@MathVisualProofs 5 ай бұрын

Glad it was helpful!

@joeshmoe1683 9 ай бұрын

Jebus.. You know, if my trig teacher 40 years ago took the time to draw this diagram, I may have actually UNDERSTOOD what I was doing, rather than just chuck out answers on a test.

@radekhurkaa8610 7 ай бұрын

That was amazing explain - again amazing - Thank you 100x^100 very much :)

@MathVisualProofs 7 ай бұрын

Glad it helped!

@Smartas599 Ай бұрын

best channel .thanks

@MathVisualProofs Ай бұрын

😀

@pradeepadhidhi5479 Күн бұрын

Great. Thankful to you

@MathVisualProofs Күн бұрын

Glad it helped

@CrazyCuteThing 9 ай бұрын

Area of a triangle 1/2 bh. 1/2 secx *sinx = 1/2*1*tanx . Therefore sinx*secx=tanx

@davidrosas2277 8 ай бұрын

Thaaaaank youuuuuuu sooooooo muuuuuuuuuch!!!!!!!!

@muchomacho2504 9 ай бұрын

Brilliant!

@MathVisualProofs 9 ай бұрын

Thanks!

@UbiytsaEditz 9 ай бұрын

I wanted to see the angles in other quadrants so badly 😅

@MathVisualProofs 9 ай бұрын

There is a linked desmos in the description. You might have to edit it but I bet you can make it happen :)

@Ninja20704 10 ай бұрын

Another way I've seen to construct tan(theta) and sec(theta) is to draw a vertical line that is tangent to the circle at the rightmost point. and to get cosec(theta) and cot(theta), draw a horizontal tangent line at the topmost point. That representation can also show all the properties show in this one. But i prefer yours cuz it's a little neater and less messy. Thank you so much. One little thing i wish you did was extend theta out of the acute range and see the trig functions in the full 2pi range, but I imagine that it might get messy, especially tan and cot. Still, great video.

@MathVisualProofs 10 ай бұрын

Yes that’s a good idea too. Also I thought about running around the entire circle but it was a bit messy and their are some technical details to manage with supplementary angles and negative lengths :)

@marceloventura6442 10 ай бұрын

I would have the same suggestion, but the way it was made in the video ends up cleaner to draw. So, the suggestion using the vertical line passing through the point (1,0) would end up being kind of an interesting side note.

@artsmith1347 9 ай бұрын

What you described is at wiki: "Trigonometric_functions.png". I like this one better. It is interesting that the tangent and cotangent sum to be the length of the line between the axes. The Pythagorean theorem gives the same equation as adding the last two identities: 2 + tan^2 + cot^2 = sec^2 + csc^2 That observation does not fall out of Wiki's illustration as easily.