Inverse trig functions: arcsin | Trigonometry | Khan Academy

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Introduction to the inverse trig function arcsin
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[@Lallushe]

Now I am prepared for you walking up the street.

[@seandafny]

lhh

[@Cube_Box]

Exactly

[@unpackingpig9144]

Let me do it in this blue colour. *Draws in yellow*

[@zakriaabbarah4623]

حبيبي والله

[@Ravenstrike721]

I thought I was confused before this video. I now know I had no idea what confused really was, until now.

[@Trisgent]

You explain it better than my teacher did! (Or maybe it's the fact I can't focus because my class is full of class clowns lol)

[@skyhopper5183]

Honestly same.

[@quonkylops]

Same.

[@RyanColquitt]

After dozing off in class multiple times, to realizing I need glasses, and just having a bad focus in general, this makes perfect sense now. Going through it step by step all at once rather than little bits and pieces in class interrupted by people talking really helps. I'm pretty sure my teacher described everything the same way too, minus using the term arcsin

[@christiancobo5324]

This is way easier than reading it in a book.....THANKS!

[@yeunju7]

wow, i talked to my teacher for about 4 hours about this, and you explain all what i need in 5mins... i love you.

[@dogwithwigwamz.7320]

I don`t know about The United States, but if I were to walk up to someone in the street over here and ask them to tell me what the sine of pi/4 is, they`d probably look at me as if I were giving birth to a helicopter ! ( Forgive the English humour ).

[@VSPG_SIVANI]

+Steve MetalHammer I came from the Khan Academy website into the KZbin page just to look if there's a comment like this on the top and LOL!!! So how many of you are like this?

[@lakshminarasimhamurthyvish9204]

+pranav turlapati 😂

[@sonalchauhan2955]

😁😁 Same in India😂😂😂

[@danielarmago6464]

*when someone walks up to you in the street and asks you about trig functions*

[@oniononiononiononion2147]

possibly

[@flour5135]

My lad! This. Right here. I have been working on these gosh darn equations for MONTHS failed MULTIPLE tests and FINALLY understand. I am a absolute noob and was truly thinking I was finding the inverse but your explanation just saved me. (Ok I’m a little dramatic but this is groundbreaking)

[@AlexisPancake]

I'm using this to study for a calc placement test. :) I'm sure I'll do fine thanks to you!

[@nexisle7508]

Just watched your intro to sine cosine tan vid and then this. I'm starting to understand this the way i wanted to understand trig. Huge respect to you man and good wishes :)

[@conconhelp]

Thanks man! I was searching for this information for hours. you're my hero

[@smoke12316]

8:12 nope, im out.

[@henri1_96]

It's a simple formula!

[@benjaminsibson8760]

FullChicken44 shut up chicken

[@Me-dx7rg]

@@benjaminsibson8760 L

[@asemnafiz]

I like Sal's videos within first minute of watching. Then as the video progresses I get more and more impressed with the information he gives and I wish I could like it more and more but unfortunately there is only one like option. Bring back the star rating on KZbin.

[@beta5770]

This is what real math is all about. Not something that we memorize a problem, and paste the exact solution in an examination.

[@TehObLiVioUs]

on the ti84 plus CE if you divide by pi on the last part of the video you get -.333333333 then do alpha y= 4: FD to make it -1/3 then since it's radians it's -pi/3 as it's supposed to be

[@nickgrqlkimd21]

Thank you ! That was really helpful

[@EDUARDO12348]

The graphs of the arcsigns look interesting.

[@krishnac62]

In this particular series, Sal used a convoluted way of explaining the concept. PatrickJMT saved my day. If it weren't for Pat, I would not have understood inverse trig functions. He didn't use the unit circle, but instead employed the graphs of sin, cos and tan. The graphs effectively explained why the domain has to be constrained (due to HLT test), etc. I hope Sal or Khan Academy notices this comment, and revamps the video.

[@abdullahalmasri612]

you are stupid sorry

[@NoirNeko333]

Love the way you say "two"

[@mybloodyvacuum]

THANK YOU SO MUCH MAN, FINALLY I LEARNED TO DEAL WITH CIRCLES

[@myaccc123]

Hey Sal. Can you do a presentation on integration involving trig inverse functions?

[@Nandine2]

OMG thank you so much sal, for responding to my request! And I understand it fully it now,

[@EaglesFastAndLow]

This is absolutely amazing.

[@scrawnytomato6582]

Sin? Makes so much sense. Thanks bro

[@iGoValkyrie]

so im in calculus 2 and this shit popped in the middle of my exam when the teacher hasnt mentionned this once, is this normal?

[@kallabotz5253]

Yeah, we have to carry all the knowledge from trig/precalc to calc and calc 2...

[@PimpMatt0]

Kallabotz Is the human mind capable of remembering all that, considering our schools teach us to take orders rather than make them.

[@just_an_empty_sign]

Yes trig functions are extremely important in calculus

[@hammurambi]

Excelent explaination. Thanks Sal.

[@Discohydrus]

I'm glad you got some better drawing software compared to your 2007 videos. That 240p resolution in MS paint was giving me a headache. My complaints about the technical quality aside... I'm using this as a study aid for a big Trigonometry test I have tomorrow, and I have to say that this is helping me memorize those trig identities and inverse functions I need because I fully understand it. I love it now. It's elegant. I needed this after 12 hours of cramming. Thank you Sal. You are a hero.

[@DivyadeepSingh1]

Ashley Abiva sin cos etc are periodic functions (i.e. they repeat there results after a specific interval of 2pie) . so, for convience, we restrict our domain from (-pie to pie) . and add 2pie in the result to genarlize the solution obtained. hope it was helpful.

[@kishoresubramani1309]

@Divyadeep Singh Why can't the range of tan inverse be [0,π] still one-one and onto ??

[@florentinosanchez3969]

Best video ever. Thank you so much for making It

[@FKX33]

Draw a right angle triangle with a missing value for an angle. Fill in the lengths of the triangle using SohCahToa. (The hypotenuse of the triangle will be 4 and the length opposite to the unknown angle will be 1). Use the Pythagorean Theorem to find the length of the missing side. Use the law of cosines, C^2=A^2+B^2-2ABcos(c), to find the unknown angle, c. (Where side C is the side length opposite to the unknown angle and A and B are the other lengths. The arcsin of 1/4 is the unknown angle, c.

[@DinoRiott]

You just saved my math grade!!!! Thankyouthankyouthankyou:)

[@ClaudioBOsorio]

Thanks a lot sal. Never stop!

[@anniemarieevans08]

Love your stuff! What software are you using?

[@VeritasEtAequitas]

Been doing all of algebra and trig on Khan, and to this point I don't recall ever seeing negative radians. Wouldn't we have to restate that as 2pi - 1/3pi = 5/3pi radians?

[@gago776]

man, by your videos you are doing a huge favor for humanity...

[@rudylawson5552]

What about when they ask for all possible vaules between 0 and 2π do you still use the range restrictions ?

[@1piecemage]

this part is simple, its pure memorzaton... can you give steps on solving identity?

[@Rboysblaster]

Check when you go to the ''mode'' screen if you have your calculator set on radians or degrees; it should be radians for this video at least.

[@xcstacy2]

I love you, I love your videos, I love your voice, I love the help you give people like me :D My prof in my first year calculus course has such a thick accent I can't understand him so I have to basically teach myself this stuff but when I get stumped you are my saviour!

[@JustinGarfield1]

Can you basically just look at the square root over 2 in the y coordinate on a unit circle and find the angle pi/4?

[@roachey15]

@Swetlana0 I'd say it's just because he has a tablet now, so it's his actual hand writing, where as before he was using his mouse to write on paint.

[@FredrichNietzsche25]

Hey sal, is it possible to have a graph of arcsin? And, if it is could you do a video on that?

[@vuthao6290]

6:01 I dont understand why theta need to be restricted. Can someone please explain it for me?

[@themin91]

Excuse me Mr.Sal, do you have presentation on converting trigonometry form to complex numbers? Urgently needed!!

[@noblessus]

Hi! I just discovered your channel and your math videos are great! Question; do you have a video where you talk about how to convert trigonometric expressions to algebraic expressions? I'm having trouble with that. Thanks!

[@ameershahul2968]

11 years later your comment got a reply

[@noblessus]

@@ameershahul2968 hurray! lol

[@ameershahul2968]

@@noblessus 🤣I thought you wont reply

[@singingsincebirthtb1418]

@@noblessus I guess you would be having kids by now

[@callitasisee]

@Artyompyandex Actually, the question would be arcsin(x)= (sqrt2)/2. This is because you are trying to find the radians. And, no, every answer there besides (-pi/4) would be incorrect. This is ok, but you have to remember that you only deal with the 1st and 4th Quadrant with arcsin. the range for both arcsin and arc tan are between (-pi/2) and (pi/2). Your other answers are not within the range. I hope I could help you :)

[@PBxTHExNIKExSBxOGx]

alg. II (adv) final tomorrow. THANKYOU!

[@carloscordova9293]

wait a minute 3:24 sin to the negative 1 (sin^-1) isn't supposed to reverse the squared 2 over 2?

[@Handle12456]

God gave that voice for a very good reason. Tnk u.

[@SonjaPond]

Ermahgerd! Thank you, Khan Academy!!!

[@Alkim_gercek]

Way better than my math teacher in turkey who cant solve 11th grade problems

[@viewlesspanda2429]

bless this man

[@droma51090]

how do you figure out-> cot(arcsin(radical x^2-9/x) ?

[@OlofTheBald]

@qsierra1 Hypotenuse can be any positive number, the angles won't change. Sal simply said it was 1 because he is assuming the unit circle's radius is 1 for simplicity.

[@star0dust8]

but the hypotenuse fro the 45 degree triangle is the square root of 2 and x and y are both 1 so why did you choose one as the hypotenuse? i find that confusing right from the start

[@lukoshke]

Thanks a lot man!

[@encryptedpenguin3220]

Thankyou so much! This was a huge help! (:

[@AOTDagents]

I LOVE this guy omfg

[@BrianJFagan]

Hmm... I'm still a little confused about how to handle arcsin with a value outside the *-1 to 1* domain. Do I just subtract increments of 2pi? Ex: arcsin(3pi/2) becomes arcsin(pi/2)??

[@strtg3y3r]

This is very helpful

[@WolvesOfAtlantis]

I live for the day this guy learns grammar.

[@thenewguy461]

@puzzlepeace19 because the function of Arcsin has a domain of pi/2 and -pi/2. If it was unrestricted then it would be a relation and not a function.

[@melvinschmid3549]

Thanks for the great videos

[@ashleyching5786]

WHY? is always the question we need to ask ourselves!

[@WishingStarflakes]

this man saves lives

[@matthewgarrett1996]

I dont understand how sin(theta) = y , but then he uses arcsin(x) = theta , meaning x = sin (theta), then restricts the x axis but refers to x now as the y axis.. can someone explain how you can just mix and match?

[@VeritasEtAequitas]

X is not always "x axis". F(x) is simply using x as an arbitrary placeholder for an input value to a function.

[@droma51090]

and by figure out i mean rewrite in a form that does not have any trig or trig inverse functions in it?

[@virtuoustex]

Thank You!

[@bkboggy]

Good video, as always. One question... my professor was doing a problem similar to yours and we were trying to find arcsin(-sqrt(2)/2). While all of us in the class said that it's -pi/4, he went on to say that it would be the same as his answer, which is 7pi/4. Now... that didn't strike me as right and after watching your video, it seems that was a correct feeling to have. arcsin(x) is the angle between -pi/2 and pi/2 (non-inclusive) whose sin is x, right? So, it's not the set of all angles whose sin is x. I wonder if he was confusing it with Arcsin(x)... which is a thing (it's the set version of arcsin(x)).

[@atom2243]

bkboggy 7pi/4 would be the same answer because the unit circle goes counter clockwise so if u sub tract or move pi/4 clockwise were the unit circle starts would would end up in 7pi/4

[@davidmetz9499]

There's a lot of confusion about this...The inverse sine function is a FUNCTION which means there cannot be more than one answer. By definition, the inverse sine function must give answers ONLY between -pi/2 and pi/2, inclusive. That's why answers such as 7pi/4 or 5pi/3 are never correct, for the inverse sine function. However, having an answer from the inverse sine function, sometimes we use that unique answer to go looking for other angles whose sine would give the same result. For example, the inverse sine of 1/2 is pi/6, meaning that's the angle between -pi/2 and pi/2 whose sine is equal to 1/2. There are an infinite number of other angles whose sine is 1/2, such as 13pi/6 and 5pi/6, and these are relatively easy to find, after we get the inverse sine answer, pi/6.

[@cvin519]

What software do you use? Me gusta

[@unsalad]

thank you, now I can tell you when you ask what is archsin on the street

[@rohans7885]

really good!!

[@handlethatsavaildable]

thank you, im never awake enough in school to pay attention

[@puzzlepeace19]

Why do you restrict it to the 1st and 4th quadrant?

[@sarablack10]

Thank you very much!

[@justforentertainment7145]

could u please explain about diploma mathematics

[@Hakeemn64]

Thank you!!!

[@dltltr]

I like how I know the answers already.

[@wetim99]

how is arcsin different from cosecant? likewise arccos to secant, and arctan to cotan?

[@itzyfan88]

I know in this case arccos(x/$md_mo)=71.565, solv for x

[@soccerman1434]

Good question, arcsin(sqrt(2)/2) is defined in both the first and the second quadrant; it is also defined in multiple rotations around the circle. However Arcsin(sqrt(2)/2) [notice capitalization] is uniquely defined in quadrants 1 and 4. We restrict the Arcsin in these quadrants so that it remains a function.

[@BruceLeefromthegrave]

You are welcomed.

[@puzzlepeace19]

Why do you restrict it to the first and fourth quadrants?

[@denizemil7559]

I’m a junior at a Turkish high school but still watching this...

[@wrxmomo1]

Yes - they are the same thing!

[@AmitKumar-ho3mr]

how to find the value of sine^-1(sine 60) ?plz solve it by using easiest way.

[@nv16123]

0:05-0:06 "I didn't want to write that thick" lol😁

[@matassadaunykas4785]

a very helpful video

[@colorsnap]

thank you!

[@qualquan]

Its a pity how unfortunate and confusing the notations used for inverse trig functions are. First the term arcsin or arctan should be replaced by the term "angle" or "theta" which happens to be the "OUTPUT". The "INPUT" (or the term within brackets) should then be simply called by the appropriate input RATIO i.e. SIN or COS or TAN etc. So Arcsin notation simply becomes theta(sin), Arctan becomes theta(tan) etc. After all, all we are being asked is that if the INPUT provided is a ratio of sides of a right triangle then find the angle or theta which is the OUTPUT. In ordinary Trig functions the INPUT provided is the angle or theta and we are asked to OUTPUT the RATIOS called SIN, COS, TAN etc. So the function is simply termed SIN theta or COS theta etc. So why not just REVERSE the function terms for inverse functions? Sin theta becomes Theta sin, Cos theta becomes Theta cos and so on. Worse than Arcsin is the SIN^-1 which gets confused with Sin theta^-1 or 1/sin theta. Why do all the teachers stick to these archaic and confusing notations?

[@qualquan]

qualquan I would modify my comment by removing the brackets around sin, cos and tan since the brackets should be used for the actual numerical values of the ratio.

[@vintagescorpio49]

qualquan It doesn't work like that

[@classicalbhargav]

qualquan how do you get confused between sin^-1 (theta) and sin(theta^-1)???

[@ishanbhatt1123]

Hi, I have question, does the arcsin (or arcos, arctan, etc.) need to be expressed in radians (or can your use degrees)?

[@pinecone7618]

arcs work on degrees

[@checkmate5338]

Mashallah brother!

[@Ren-ITe]

We really need to keep this man off the streets.

[@GreetingsItsEva]

I hate math class these days. I go into school feeling depressed and stupid and come home frustrated because of my grades and my inability to complete my homework with out profuse outside instruction. I've never been in a situation where a little hard work didn't help me improve.

[@winkawak]

wish i have you right now instead of my trig teacher

[@richanddarksbane1439]

really really good explaination

[@Teymur69420]

I agree

[@Rboysblaster]

Yeah, funny thing that it is as far as I know. Maybe it's not practical to work with multiple periods; if you know 1 you can work out the rest. But that does not mean the other periods don't or cannot exist, and certainly it's just wrong to say f(x) cannot return multiple values! Of course it can: f(x) = x² + 6x + 8 = 0 just to give an example :P

[@joviefokou4400]

please help me arsin(2/3).arcos(-2/3) how l can resolve that.