Why are Tangent & Secant given their names?

[@SP-qo1so]

I’m up at 0235 watching these videos. I’m 29, haven’t been in math classes for like 8 or 9 years, have zero use for this information, and this is still fascinating. You’re an amazing teacher.

[@paulreader1777]

Agree with your opinions of the subject and Eddie's presentation but curious about why you have zero use for the information.

[@SP-qo1so]

Paul Reader tangent and secant have about as much use in my line of work as male nipples do in everyday life. It’s superfluous info that has zero practical application for my job. Don’t know how else to say it.

[@paulreader1777]

Ok - thanks for the reply and sorry for my intrusive question.

[@SP-qo1so]

Paul Reader not intrusive whatsoever, sir.

[@curtbentley]

@@SP-qo1so One day you may have a kid...then this stuff comes back with a vengeance, haha. I agree, though, this teacher is first rate!

[@swag-mexico-gucci]

THE PERFECT FREEHAND CIRCLES I CAN'T

[@sahibakaur2930]

When I watched this video, I felt that spark that I feel when I finally truly understand something without having to memorize. Thank you for allowing me to feel this through your wonderful teaching!

[@tahmeedchowdhury0007]

Just realized this can also be used to prove the identity tan^2(x) + 1 = sec^2(x). Brilliant teacher.

[@santoriomaker69]

Also, the names make much more sense. tan θ is a part of a tangent line (so does cot θ, which somehow not mentioned in the video, it's the measure of line AX in the video), sec θ is a part of a secant line. A secant line is any line that intersects two points of a circle.

[@SuperFerdie1965]

But it only proves it for acute angles.

[@MelonMediaMedia]

you can just use a normal right triangle, but okay

[@DanksterPaws]

@@SuperFerdie1965really?

[@youtert]

He's really getting off on a tangent with this history lesson.

[@saykhia]

I secant this motion.

[@telsys]

I co-sine to this.

[@siddheshmadkaikar1645]

preparing from your videos for a competitive Engineering Exam in India, and suddenly math has become so interesting.

[@ermonmclovin8002]

Im attending engineering courses at university and ive never studied trigonometry in my entire life. Here in Italy, teachers dont care of math, they just teach greek, latin, history and humanistic stuff. Now im in a hard situation, and thanks to you im learning trigonometry not just as abstract formulas that i do not get

[@sammymohamad1250]

I received very substantial math education in Mexico, and I understood nothing. If I only had professors like this, math would've made more sense. So feel good about it, at least you didn't wast countless precious hours of your life like me lol

[@DarthZackTheFirstI]

wish math professors at the uni would be like him and actually teach instead of only giving new mountains of challenges without explanation :p

[@wenhaohuang5053]

Ti capisco

[@pinklady7184]

Arto Zeronian I will check out Professor Rob Bob. Combining Eddie and Professor Rob Bob will make our brains swell within short time.

[@Macatho]

Say what? This stuff is taught when you're like 15-16 yo, at least here in Sweden.

[@albertoolmos21]

Tangent from Latin 'tangere' to touch a point, without intersecting it. Secant from Latin 'secare' to section, divide, cut something. This is why they are given their names, the rest is a mathematical convention, still sine ('sinus' = hollow) cosine (sine complement) derive from Latin too. Mathematics, as well as all sciences, are easier when you know what you are talking about.

[@DeJay7]

Actually, that's why they mean what they mean. But tangent is a perfectly fine word even outside of mathematics, and its meaning is the same. Questions was, why is the ratio opposite/adjacent called the tangent? Here's why.

[@risegiy5647]

this vid shows why trig ratios are named tan and sec

[@rosswaring2835]

This guy just loves what he does. So clear and well explained with such enthusiasm. Very fortunate students to have him.

[@reintsh]

Sorry mr. Woo, you didn't explain where the names came from, so I'll do it. "Tangent" means "touching" (cf. "tangible") and "secant" means "cutting". Look at at your drawing once again and find the touching point and the cutting points. The latter are called "intersection", aren't they? Hey, SECtion, SECant?

[@ViratKohli-jj3wj]

Are you gay?

[@FreemonSandlewould]

TY

[@junkonakamura3441]

Nice perspective to look at it. Kudos. 👍👍 Gratitude.

[@StolenHandel]

He actually mentions both he just does it in passing. Check around 4:00

[@jorgeuni2]

He is very ‘teacher center’ . I don’t know much about education in Australia but certainly he would fail teaching in USA. He is just a lecturer with passive students

[@TheSidyoshi]

I am stunned, absolutely stunned. How is this possible? I have a decent grasp on abstract algebra. I was good at maths in school. I never knew where these names came from. For me tan was defined as sin(x)/cos(x) or opp/adj. I figured it had something to do with the tangent of a circle, but wow. I'm speechless. You can reason out a lot of trig identities geometrically, just from looking for similar triangles around the unit circle!!! WOW!!! I'm a little surprised how far in life I've come with this huge chasm in my knowledge. Now thanks to you it's been fixed up. It's a little unnerving... what other holes are there in my knowledge?

[@LuigiElettrico]

Same here... this changes my point of view on those functions... even though i know them and use for years...

[@Siflo98]

Same here bro. I’m a second year at my engineering school from France and I didn’t know what tan x represented geometrically speaking....

[@swazeyyy]

The education system doesn't actually care if you understand a concept. They want to teach you the easiest way to remember how to do the work so you get good scores and they get more grants

[@Jagannath.Behera]

@Rusty what the hell you are speaking man ? Dont you want to be a human with cognition, but a brainless computer with rote formulas?

[@Jagannath.Behera]

@glyn hodges great bro !! This is the best of the best idea, and it must be implemented in all educational institutions around the world.

[@HeathenGeek]

I know my way around a trig textbook, nobody ever explained tan and sec like that before. Very, very nicely done, thank you.

[@coldmine9480]

Guess what, apart from straight lines, he can make perfect circles 😂

[@RangerCaptain11A]

when i was earning my math degree there was a big push for 'writing across the curriculum' and the history of mathematics. when i became a teacher, i always told the back story of the discoverers, and the times they lived in that necessitated the mathematics, always trying to dispel students' notions that math came from thin air. if you're interested, go find out how rene descarte invented graphing -- its a doozy.

[@shubhrajit2117]

Thanks for your explanation! Sine has also got a similar story. My TB says "the idea of sine days back to Aryabhatta who called it jya or Ardha-jya that literally means half-chord". This is quite apparent in a unit circle.

[@nicholasyap9000]

Mind offiicially blown... How can someone be so good at explaining? Omg if he was my teacher i would have fared off so much better in math wts

[@samuvisser]

How can this guy draw such perfect circles... It's just not fair!

[@AngelTiel]

Most people don't know what a secant is. ( It's a line that intersects with a circle twice-the line segment between those two points is a chord)

[@kappro1517]

So a secant is essentially a chord produced?

[@carultch]

@@kappro1517 Secant lines are infinite length, and intersect the curve at two points on it. Chords terminate at the two points where they intersect the curve, and are line segments of finite length, rather than lines.

[@carultch]

@@kappro1517 Chord is to secant, as diameter is to the line through the center of the circle. The diameter line segment is a special case of a chord.

[@carultch]

Also, the line segment of length secant, is not really a secant line as circles are concerned. It is coincident with one special case of the secant line, whose chord is the circle's diameter, but the line segment in question doesn't touch the circle twice.

[@qiangqno1]

wish I always have that much passion teaching every day!

[@teiyaamuah]

This is one of the teachers. He makes look so easy, he is one of my best teachers. Top 5

[@ianmontgomery7213]

Tangent 1590s, "meeting at a point without intersecting," from Latin tangentem (nominative tangens), present participle of tangere "to touch," from PIE root *tag- "to touch, handle." First used by Danish mathematician Thomas Fincke in "Geomietria Rotundi" (1583). Extended sense of "slightly connected with a subject" is first recorded 1825. Related: Tangence; tangency.

[@draguernel1457]

First used by Danish mathematician in 1583?? How can you erase centuries of work, especially arabic, who made a whole math speciality from trigonometry?

[@Yesindeed-v5m]

the way you drew a circle at 2:05 is unbelievable

[@vari1535]

But secants don't necessarily have to pass through the center...

[@danishajaib1923]

I never thought I'd ever be watching math videos for entertainment.

[@GigasnailGaming]

algorithm strikes again with a brilliant educator. love it. good stuff.

[@martymoo]

I always learn something from Eddie Woo. What a great teacher!

[@Wanderibbon]

Extremely useful 🎉

[@atil4]

As simple as it is, I have never got this explanation. Thank you!

[@jhg8464]

the way i have always liked to look at tangent is that it is the slope of an angle in direct variation it is cos theta/ sin theta, which in the unit circle is just y/x, a slope if you want to find the rate of change of a line that creates a 60 degree slope with its y=b line, you would do y=(tan 60)x+b

[@upliftingcommunity2465]

This is great! I tutor math for the ACT and I’ve always told people not to confuse tangent (with circles) and tangent (with triangles). Now I can show them it’s the same!

[@sortehuse]

I was never thought this is school. I wish I was.

[@francisp9122]

In a unit circle, you define an angle from the horizontal axis going counterclockwise. Your theta should be negative theta.

[@LukePettit3dArtist]

I'm finally understanding where Tangent comes from but Dude! you need to stop using theta and Q in the same effing drawing as you're toying with my dyslexia and making this harder to read than is necessary.

[@kofi_haven]

Please why do you choose unit circles to prove the trig ratios?

[@tccccccc810]

Im in calc 3 in engineering undergrad and i cant believe youre the first person to tell me this. Maths are awesome.

[@raymondfrye5017]

You have no idea. When you have to apply it like a physicist then you'll see how awesome it really is. Regards

[@sebastianbalbo1906]

Antiderivates(b)- Antiderivates (a) / b -a can be converted to formula where we can use the TANGENT IN DIFFERENTIAL EQUATION )

[@tuckerave1]

Awesome teacher! Thanks

[@Shake_Well_Before_Use]

Those are beautiful circles

[@mrbg2138]

best teacher ever !

[@aidanmcdonagh7861]

This helped me understand tan and sec way better 👍

[@RavingRunner]

"The length of the tangent"

[@ahmetyetkin2898]

he just showed what tanx and secx is on the unit circle? we already know that i want to know where does the name come from? why secx is 1/cosx and not 1/sinx and cosecx is vice versa

[@விஜய்-ச4ட]

He is explaining why tan0 ratio and sec0 ratio are given their names. Not how tangent lines and secant lines got their names. For your second question he explained it in the video...

[@lifeisbeautiful7311]

Mindblown

[@caryboy2006]

I would think that most people would not know that trig functions are scalar. Sine and cosine and tangent are lengths. They are expressed as a percentage of the length of the radius. Example for 60°: the cosine is 0.5 of a unit circle. If your radius is 7 km, the length of the cosine is 3.5 km.

[@murraywilloughby7116]

I asked my University Calculus Professor this exact same question and he didn't have a clue. He also thought I was sort of demented for having asked. I might have been a Physicist today, but I walked out of the class.

[@mimzim7141]

never used sec in my studies and when learned about it thought it was useless and that you can get same info with cos. but seeing this gives sec lot more sense.

[@3rddegreeyt144]

Sir did you had read the whole Principia cuz these are the same diagrams that were in that book but it is complicated to understand genius

[@Carrymejane]

This man is really attractive

[@aishwaryajangir2909]

so tangent was defined and derived before trigonometry?

[@ianmontgomery7213]

yep it originally meant "meeting at a point without intersecting" so it didn't necessarily have a length

[@raymondfrye5017]

No, tangent and secant came afterwards in Greek and Latin. Trig was existent THREE THOUSAND YEARS BEFORE Greece and Rome in Babylon.

[@hidude8095]

I thought secants were lines inside a circle touching 2 points in its circumference

[@redangrybird7564]

I see, a secant line is to a circle what a cut is to a pizza, fantastic!

[@saniachoudhari]

Amazing teaching tricks!

[@RealSlopeDude]

In the US we would call that angle AOQ or QOA.

[@syth-1]

This is rlly good but now I'm left confused how this script works to draw a circle Essentially it uses pi * 2 to get ratio of a full circle, multiplied by 1/resolution * iteration (Resolution is the number of vertex, while iteration is what index of vertex count we're adding - using this you can get the % of circle we're at) All of that gives an angle for our circle, fairly easy to understand. . The next part: place a vertex at x: cos(angle) * radius, y: sin(angle) * radius, z:0 What is cos and sin doing to get the x and y position. . Cos is getting length as shown in this video, but if that's length in any axis direction what makes it correlate to x axis, if it was a vertex at 0, 3, 0 (a vertex 3 units up from the origin) you'd still have a length of 3(??) while x is 0. . ;-; maybe I'm over seeing something important, Srry if it doesn't make much sense

[@kaifscarbrow]

cos is length in the x axis, sin is length in y axis. At 0 3 0, the length is 3 yes, but in the y axis not x axis

[@argonwheatbelly637]

Need to mention the exsecant and the versine, and that sec = cos + versin + exsec. Then you go into spherical geometry, and work with haversines, and talk ease of navigational computations by tables--pre-calculator age. ;-)

[@raymondfrye5017]

Yeah. I had to learn how to make log/exp, and circular function tables with series and other techniques to solve problems. It takes time to do these things but there is nothing like a man who masters his basics and can apply them. Regards

[@drewfasa]

Mind blown...

[@reubenmanzo2054]

What's to stop the secant from being the other side of that triangle?

[@jayaseelanpatchy9132]

Chinese don't need a compass to draw a circle

[@eseheitor2035]

Those circles though...

[@jeffersonevanderrocha8323]

Hello sir, since OQ is the secant it means that secants are the hypotenuse of whatever angle you have in a circle? Thank you, hoping you would response.

[@charlieschulz8144]

okay yes the math is cool... but his drawing skills? out of this world. Those circles are perfect. The length of his secants extend perfectly to where the tangent will go. wild

[@argonwheatbelly637]

He's close to being Giotto di Bondone good.

[@johnlennon612]

Thank you.

[@sociajl751]

great explanation. Thanks!

[@WhitEagle7]

where is the explanation of why they are given their names?

[@nightsky5037]

doesn't a secant line pass through 2 points in a circle?

[@paulg444]

Eddie is great !!

[@sachinkhot459]

born mathematician..passionated about math

[@baltimoredude1]

Doesn't a secant cut a curve at two points? Your example cuts are at one point.

[@kagazki7026]

You're telling me I could have remembered that sec was the reciprocal function of cos by simply remembering the third letter of sec and NOT mumble it over and over throughout my tenth grade????!?!?!

[@photonicsauce7729]

Didnt u have confusion for cosec also in that method, since even cosec function ends with c

[@kagazki7026]

@@photonicsauce7729 i did. :( I memorized it but it wad so hard to remember. That's why I didn't like maths.

[@mohammadowaiskhokhar2318]

How does he make circles like thay?

[@shantanumulajkar2471]

Hi! can you please explain why tan 90 is infinity?

[@surrealisticinfinity2895]

Its not defined. Tan = Sin/Cos. If cos value is 0, which is the same as cos 90 degrees, you cant divide it. Same with 270 degrees which also have a cos value of 0. You cant divide anything with 0. Also think about it, if you have a tangent drawn from (1,0), and you draw an angle with a extended line that hits the tangent further and further up the greater the angle becomes. Do that until you hit cos 90 degrees, which is the same as the y-axis. It means the two will forever run parallell to each other. They will never ever cross thus it is infinate and not defined. Hope you understand what I mean lol.

[@johnwalker1058]

Based on what Eddie is teaching in this video, a wider central angle in the circle will consequently require a longer tangent line segment to meet the extended side of that central angle. Keep widening that angle, and a longer tangent line segment is required to meed that angle's side. At 90 degrees, the side of that central angle will shoot out of the circle exactly parallel to the tangent line. Thus, in the case that the central angle is 90 degrees, the tangent line segment must travel infinitely far to attempt to meet the angle side it will never meet since they are parallel to each other. (Approaching 90 degrees in that central angle would require a VERY long tangent line segment, but eventually, the angle side and the tangent line segment will eventually meet).

[@hasnain9654]

Tan90°=sin90°/cos90° .... Sin90° equals 1 but cos90° equals 0 so 1/0= Infinity hence Tan90° is infinity. Got it?

[@JustLeftLeg]

@glyn hodges nope, youre wrong. According to Lobachevskii geometry parallel lines will cross... 2 times: from left and right. ;)

[@JustLeftLeg]

@glyn hodges FeelsBadMan

[@roganferguson]

This is NOT satisfying. A secant line typically cuts a circle in exactly two spots, and yet this secant only cuts in one spot, yet you act as if that is a perfectly good reason to name it secant.

[@abhyudayshardulsingh5159]

Awesome

[@kalyanborpuzari6448]

Can you write a bigger letter and numbers

[@shashank_kishore_]

❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

[@yuurishibuya4797]

What about cotangent?

[@kriskringleecommerce1367]

Thank you!!!!

[@Americabeatz]

thanks dude, i get it now.

[@pritigajjar4105]

But what if it is not a unit circle ?

[@carultch]

If it is not a unit circle, then you have an r-factor in each of the lengths in question, referring to the radius. On a unit circle, the coordinates of each point are given by x=cos(theta) and y=sin(theta). When it is something other than a unit circle, the coordinates of each point then become x=r*cos(theta) and y=r*sin(theta).

[@xpbatmanqx5535]

@@carultch turning them into polar coordinates in the process right?

[@carultch]

@@xpbatmanqx5535 Yes, you will recognize that these are also the formulas for converting polar to rectangular coordinates.

[@xpbatmanqx5535]

@@carultch thanks

[@sanchitverma2892]

Why is this video 4:19 minutes long it bugs me

[@CHEESYhairyGASH]

Thanks

[@MalleusRegum]

Then where do "arc-" names come from?

[@DarthZackTheFirstI]

its the invert of cos 90. e.g.: if you type into your calculator cos 90 you get some number. if you calculate without the angle to get an angle you get a number which can be used with arc-tan - (tan -1) - ( or cos, sin) to get the angle from the calculator. so it must mean invert or something or some kind of circle to get from one point to the other (arc). now i just need to prove that....google isnt the wisest on this :p

[@johnwalker1058]

Recall from geometry that the angular measure of a circle's central angle is equivalent to the measure of the arc length of the arc it subtends. (The measure of a central angle equals the measure of the arc it contains). Now inscribe a right triangle into one of the quadrants of a circle, where the hypotenuse of this inscribed right triangle is also the radius of the circle containing this right triangle. From trigonometry, the inverse trigonometric functions use side lengths of a right triangle and the special relationships between them to derive a missing angle measure within that right triangle. Using the inverse trigonometric relationships of a right triangle, one can find the measure of an angle. Doing this in a right triangle inscribed in a quadrant of a circle will also happen to yield the measure of the central angle that is formed between the hypotenuse and horizontal side of the inscribed right triangle. By the theorem mentioned in the beginning of this comment, that central angle measure reveals the measure of the arc that is subtended by that central angle. Thus, when inscribing a right triangle into a quadrant of a circle, using the inverse trigonometric functions can reveal the measure of the arcs surrounding them. Doing this for inverse of sine yields the "arc length of inverse sine" (arcsin), while doing this for inverse of cosine yields the "arc length of inverse cosine" (arccos), and doing this for the inverse of tangent yields the "arc length of inverse tangent" (arctan). Hope this helps! Sorry for being a little long-winded.

[@raymondfrye5017]

@@johnwalker1058 What's that?...Long-winded? At least it was enjoyable and COOL-air, unlike HOT-air balloons like members of Congress,tge Executive and other politicians.

[@davidwilkie9551]

Form follows Functions of this e-Pi-i, AM-FM communication mechanism in Singularity positioning here-now forever Holographic formatting, and there's a topological orientation appropriate approach to the meaning of the chosen observable objectives. In perspective, a particular identification of the metastable unity, and mathematical methodology formulae used in component assembly.., so in the context of Actuality for this video, how and why the temporal condensation format has come to this structure, is lost in history. It's normal/typical for lessons to reiterate continuous creation connection function in CCC format, e-Pi-i QM-TIMESPACE, re-cognition Principle. ("Mind over Matter" general existence, be here now)

[@paulfrischknecht3999]

sec, ces, cos! I totally got it! Thanks.

[@ramyresdavid6539]

1:25 theetah

[@hids746]

how aq become tangent...till today it is radius for me???? bit confusing...reply whenever u c ds plzzz

[@saddamc.h.5639]

You might be confusing the theta sign for the letter "Q"

[@andrewbevan4662]

So much background noise...

[@jgostling]

Yeah, it's called a classroom! ;)

[@andrewbevan4662]

@@jgostling do you what age the pupils are? Is it a compulsory lesson or have they chosen to do the subject?

[@buggaboo2707]

Still completely unintuitive that inverse of sine is cosecant and inverse of cosine is secant... one would guess the "co's" go together :/

[@carultch]

You should use the word reciprocal in your statement, rather than inverse. Inverse means something completely different than reciprocal, for functions in general. Cosecant and secant are reciprocals, arcsin and arccos are inverses. I do agree with you that it is non-intuitive that the co-prefixes don't line up with the sine and secant functions as they are defined thru reciprocals. You could still preserve the meaning of "co means of the complimentary angle", if in an alternate history we defined 1/sine to be secant and 1/cosine to be cosecant. In any case, the reason why 1/cosine is defined as secant, rather than cosecant, has to do with this diagram: i.stack.imgur.com/rLFW3.png The line of length equal to secant, is adjacent to the angle theta where it originates from the circle's origin. By contrast, the line of length equal to cosecant, is adjacent to the complimentary angle of theta.

[@buggaboo2707]

@@carultch Yes, I agree... please replace my use of inverse with reciprocal :)

[@nurulhidayah2143]

why this topic in addmaths :')

[@beaurottier8271]

May i go to the bathroom please?

[@HildmansBookEmporium]

Secant, seek. Tangent, tantrum.

[@HildmansBookEmporium]

Yeah, yeah.

[@cobyup10]

Good lesson, but the mispronunciations are blasphemous.

[@HildmansBookEmporium]

Just kidding. We know why.

[@HildmansBookEmporium]

God, I don’t care.

[@quandarkumtanglehairs4743]

Perfect. Thanks!