Inverse trig functions: arctan | Trigonometry | Khan Academy

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Understanding the arctan or inverse tangent function.
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Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!
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[@cassied9327]

I was really starting to get down on myself because I could never answer the trig questions I was getting asked on the street. Thank you Kahn academy. I no longer walk the streets in shame or fear.

[@keenanmurphy4521]

But sir. What is the arctangent?

[@maskedmarvyl4774]

I hope that it becomes as easy as pi for you. You'll never have to fear going off on a tangent during your walks again.

[@ammo381]

still waiting for that one guy to come up to me and ask me about inverse functions lol

[@slimyfister]

Man's brought a rucksack full of oranges to school and needs us to estimate the vol of his rucksack given it fits 32 oranges. He doesn't worry what we think, he's living his best life

[@supravaroy9971]

Sorry man,but studies r not for u guys :)

[@JosueMartinez-ww1vj]

If you work in architecture, engineering, etc you will definitely be asked.

[@thepm517]

@@JosueMartinez-ww1vj hello, I m from wakanda

[@monsieurLDN]

@@thepm517 same but I got lost in paris without acces to my wealth. If you give me 500$ I will handsomely thank you with a portion of my riches

[@michaeladams762]

It was a dark, stormy night. Your car broke down and you are walking to the gas station. You see a man in the distance. Clutching your umbrella, you increase your pace. As you get closer, you see the man more clearly: glasses, khakis, and a button-up shirt. You wave, trying to be nice but not trying to initiate conversation. As you pass, he steps in front of you, blocking your path. "Y-yes?" You ask the man as your heart begins to beat faster. He stares at you for a second, but to you it feels like minutes. Every possible scenario runs through your head in these short moments. Mugging? Murder? Kidnapping? As you ponder the possible ending to this encounter, he begins speaking. "You. What is the arctangent of minus one?"

[@akankpattnaik]

While I'm reading this I'm laughing so hard.xD.

[@calebpittman1794]

this guy is literally gonna be accredited with me passing precal

[@hanniballecter5383]

You mean arccredited :v I'm out

[@uniqueh5203]

Can't believe we have been taught all these years in science school to use the inverse function on calculator to find out angle value without explaining to us from where it comes. Thank you so much Khan academy

[@hira_its_ira]

HELP I'M GETTING MUGGED BY A MATH TEACHER!

[@scottwhiteside1685]

Can I have this dude as my PreCalc Teacher instead?

[@Barnekkid]

I think these videos are wonderfully informative. I appreciate their direct approach and I think this is a refreshing departure from the usual obtuse method found in the majority of textbooks.

[@PumpiPie]

Dont know what street you are hanging out at. But it is sure a weird one xD

[@fedodedoo]

many thanks to you my friend, i swear i learnt more and better here than in class with our prof. thanks a lot god bless you

[@MrTiago94]

"tan= slope of a line" mind=blown O_o

[@hopelessdigger]

So blown

[@To-mos]

You're rise over run explanation made so much freaking sense

[@karanpannu5834]

0:54 Sal the kind of person to ask trig. from species walking down the streets.

[@tetyanazlatova7446]

“There is a lot of walking up on a lot of streets”😂 I think I’m way too tired cuz I laughed too hard at this.

[@usernamesmike]

Great review before exam! Appreciate!

[@Meganerdbomb]

This is great! Can you do one on finding the derivatives of inverse trig functions?

[@BioPycho24]

your range is -pi/2 < y < pi/2. And 7pi/4 is gretaer than pi/2.

[@JoeManGuy23]

Hey Sal! I was just curious since I started to notice a difference, did you update your software or something that you are doing these videos with? Just curious, they look amazing now, and much easier to follow!

[@Pete-Logos]

@3:19 This should be #1 trig video: h=1, sinθ = y cosθ= x tanθ = slope (y/x) My life would have been so much easier.

[@bmisawa3750]

So fcking true.

[@jvgough]

wow! the connection between slope and tangent was not as apparent as it is now

[@qualquan]

An easy way to remember inverse trig functions is that in trig functions the INPUT (or what goes between brackets) is THETA or ANGLE whereas in inverse trig functions the INPUT is sin theta or cosine theta or tan theta etc. This reversal of INPUT causes reversal of OUTPUT. That is why the OUTPUT of inverse trig functions is always THETA or ANGLE.

[@arf101088]

arctan finds an angle of a triange given a slope. got it

[@SuperRiz1995]

Thank you!!! My Math teacher is incompitant and bad at her job, you are my hero. I have been watching all of your video's and you explain it 9^x (pick a big number) times better than her. If it wasn't for you I would have dropped the class. Thank You!!!

[@XStarChicaX]

I am completing my degree in Civil Engineering, and every so often I need a review of the basics to apply toward my upper level classes. I LOVE this particular Math instructor's videos. Not only do you know your craft inside/out, but you can present it to a wide scope of students so that we all get the concept behind it--without making it seem harder then what it really is!! THANK YOU.

[@nkpen22]

holy- this is from 10 years ago

[@SapereAude625]

@@nkpen22 12 already

[@woodenjaw]

Thanks Sal, i was so worried about my next Cal exam.

[@maxerrixon1267]

I love the "if someone were to walk up to you on the street and ask you" introduction. That's such a relatable scenario! Actually, I wish people would actually do that. Maybe a fun way of getting to know people :-)

[@TheseAreugly]

Shawty got arctan I ain’t gonna lie

[@snownestling]

boards of canada led me here and I learned something!

[@taylorswizzzle]

If someone to walk up to me and ask what is the Arc sine of x...because that usually happens to me...

[@taylorswizzzle]

Wow look at me 7 years ago trying to be funny

[@ishaanedits4230]

@@taylorswizzzle ik

[@jaredmartinez4585]

@Zach Stein, perfect way to explain it, thanks for the help!

[@syth-1]

I have finally found the answer, Thank You!

[@bsivoljr]

Your so skilled. Are you a professor? Any higher level pursuits you have in Science, Math?(Physics, Math, Engineering)

[@shoesies05]

thank you thank you thank you! you are such a big help!!!

[@CrazedDoodler]

Ya know, it's interesting that I know this stuff... BECAUSE I WAS TAUGHT IT ABOUT A WEEK AGO IN MATH, AND YET THE TEACHER GIVES ME THIS TO LEARN ABOUT. Education these days, right?

[@joltjoltjolt]

Arctan can be an infinite amount of numbers, specified by pi/4. But in these questions there was no specified domain, so we assume the they want the principle values, which for tangent they are in quadrant one and 4.

[@luca5900]

i am a big fan and thank you very very much for posting these videos... but when you draw a circle could you please your the "circle tool" just because it makes things a little neater :p. thank you

[@StaciAnne215]

What about evaluating a problem like tan(arcsec x/3) - how do you solve this?

[@ambientscience2951]

I have to learn many things before this the is I was just a hard drive before this and now I am becoming a human brain I realised I never learned mathematics actually I just mugged it up and spilled it in exam

[@powdertoy2]

why can't the arctan be in the 2nd and 3rd quadrant?

[@refraggedbean]

great for learning what I could not due to standardized testing, also why are people walking up to people asking them complex math questions?

[@TurdFurgeson571]

I see standardized testing also caused you to neglect the material covering attribution bias.

[@Clotonervo]

You should be a life guard, because you saved my life.

[@sansamman4619]

One day I will watch all your videos...

[@virginialikesyou]

I love you so much!

[@JesusNails8518]

what is this program you are using in the video?

[@refraggedbean]

It is called SmoothDraw, at least according to wikipedia.

[@daveedoff6258]

Still didnt tell me how to solve for x 😑

[@pmw3pmw4]

how to do arctan on mathcad?

[@Faery18]

PLEASE CHK UR INBOX. I'M DESPERATE. THANK U

[@quinndepatten4442]

You know I'm rolling up asking you what the arcsine of x and you'd better be ready.

[@KJ7JHN]

I still have and use my ti-85!!

[@Siikient4]

sin(arccos(3/5) I know the answer but i have no idea how to figure it out. Can you please help me!

[@danwest9900]

Khan Academy: Pretty good video. Thanks for posting. My only criticism is the triangle diagram that you started drawing at 2:12. Are viewers supposed to be able to clearly see and understand what is happening in that tiny, cramped up diagram? My advice: pay more attention to making your diagrams more large and centered closer to the center of the frame. It doens't do any good to see words written all over the screen and then try to squint our eyes to see a squished up diagram. Give yourself more room for those diagrams. They are CRUCIAL to your explanation.

[@DCVolo]

How to differentiate normal people to Khan people? Normal people - "what time is it?" Khan people "what's the sin of your clock? Oh its only PI over 6 sir"

[@pisanza123]

it's easy more than GAT and PAT1 (GAT and PAT1 is test for pass in high school education Thailand ) because you can see Math Olympic in GAT and PAT1. it' so stress out

[@chocowell_]

what kind of problems would be solved with trigonometric ratios? i can’t think of any place of where they would be used

[@timon7855]

Well, to give you an idea: I'm currently working on programming a drone that has to balance itself out to keep stable, and to know in which angle it is currently, it has an accelerometer. However, that does not give direct angles, but it gives you accelerations in x, y and z directions. To convert this to an actual angle in degrees, you have to convert it using the formula: psi = arctan(accelerationX / accelerationZ) * 180 / pi. There are many code libraries for that, but if you want to do it REALLY quick, you have to implement it yourself. And then you need to know this! So: For stabilizing airplanes, drones, ships and other vehicles the arctan is super useful!

[@abeerabeer115]

شكرا

[@jaredmartinez4585]

So why is 7pi/4 not an acceptable answer?

[@thegettokidZz]

here's an idea, let's give you an example that skips over all of the math behind the equation instead of an example that actually goes through the numerical principles behind why the answer is the answer. Let's give you a 45 45 90 triangle so we can skip all the reason behind why this is true and just know that the sides are of course equal and the angle must be 45.

[@crihs6108]

Is there any proof of arctangent?#

[@laxitbhagvandassenghani9797]

so confusing.............¿

[@ChaseBarron]

i fucking love you please take my teacher's job

[@ghostly65]

@MrTiago94 yup and soh-cah-toa= sacajewea's cousin

[@meanmole3212]

8:28 for some reason "well I just said it" made me lol. The tone carried a tiny bit of "were you listening anything at all, you **** ****" with it :D

[@helenacolley5680]

Why is arctan(pi) not 0?

[@juansinaaaaaaaaaaa5402]

because tan(0)=0 not pi

[@Teknet14]

CowboyHiha tan(180) also equals 0

[@alboshajdari3316]

You cannot say "arctan(pi)" because it is just wrong You can ask of "arctan(-1)" or "arctan1" to find the degree and radian (in this case pi/4) BUT you can ask arctan0= pi or even 0 and 2pi, actually 0 and 2pi are just the same in EVERY CASE

[@saurabhs4743]

Helena Colley in other words why tan 0 is not pi! . tan means slope. sin is y, cos is x, so for tan 0 means, traingle of height equal to 0, nothing but x-axis.. tan 0 will be 0 since sin/cos = 0/ something = 0. and pi is 3.14 which means slope is positive and not 0

[@qualquan]

Albos Hajdari arctan(pi)=72.34 degrees or 0.402 radians

[@mujtabaalmodhafar1027]

whats inverse tangent?? is het 1/tan?

[@MrClarktom]

1/tan is cot. inverse tangent is tan^-1 on a calculator.

[@Felipe917]

If you walked up on me in the streets asking that, I'd tell you that you was in the wrong neighborhood, werd!

[@emmav5641]

Thank you!!

[@Y0NGERS]

6 people don't like walking up streets =P

[@SKINNY15lol]

howd you get root 2 over 2? you dont explain it. Why is the line -1? You dont explain it. why are there 2 45 degree angles? you dont explain it. I watched this vid 5 times, and i have no idea how to solve the simple equation arctan -1 Step by step instructions would be better, so no one would have to feel the pain of not understanding a step. Don't assume we know everything

[@ClickHereNOT]

Well, first of all you have to multiply the equation by 1. Secondly, apply maths to solve the equation. And there you have it. Hope that helped :)

[@maryhasak992]

This video didnt help me at all :(

[@SIGHTlNGS]

@ 00:29 he drew a weiner.

[@StAndAl0neCompl3x]

@SKINNY15lol Don't assume everything is going to be spoon-fed to you. If you can't get it as simple as it's explained here, you have a problem - not him. Go back and review some previous videos instead of waiting for someone to hold you by the hand.

[@christiancobo5324]

You sound like Obama...the only difference being you know what you are talking about Sal.

[@GodLove-dv3os]

NOT HELP FULL