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Inverse trig functions: arcsin | Trigonometry | Khan Academy

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Introduction to the inverse trig function arcsin
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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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Опубликовано:

30 сен 2009

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Комментарии : 252

@Lallushe 9 лет назад

Now I am prepared for you walking up the street.

@seandafny 9 лет назад

lhh

@Cube_Box 4 года назад

Exactly

@unpackingpig9144 6 лет назад

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

@zakriaabbarah4623 3 года назад

حبيبي والله

@Ravenstrike721 4 года назад

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

@RyanColquitt 6 лет назад

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

@dogwithwigwamz.7320 8 лет назад

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 8 лет назад

+Steve MetalHammer I came from the Khan Academy website into the RU-vid 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 8 лет назад

+pranav turlapati 😂

@sonalchauhan2955 3 года назад

😁😁 Same in India😂😂😂

@Trisgent 10 лет назад

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 2 года назад

Honestly same.

@quonkylops Год назад

Same.

@slenderman4378 Месяц назад

What are you doing now in your life

@yeunju7 14 лет назад

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

@christiancobo5324 11 лет назад

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

@danielarmago6464 4 года назад

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

@oniononiononiononion2147 3 года назад

possibly

@calamar1e320 15 дней назад

Just one up them and start asking questions about literature and grammar rules.

@smoke12316 6 лет назад

8:12 nope, im out.

@henri1_96 4 года назад

It's a simple formula!

@benjaminsibson8760 4 года назад

FullChicken44 shut up chicken

@Me-dx7rg 3 года назад

@@benjaminsibson8760 L

@iGoValkyrie 7 лет назад

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 7 лет назад

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

@PimpMatt0 7 лет назад

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

@AlexisPancake 11 лет назад

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

@flour5135 2 года назад

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)

@ericj199 2 месяца назад

Just wanted to ask, Are Inverse trigonometric Fns in any ways similar to logarithms?

@DivyadeepSingh1 10 лет назад

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 5 лет назад

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

@TehObLiVioUs Год назад

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

@beta5770 12 лет назад

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

@Discohydrus 10 лет назад

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.

@krishnac62 6 лет назад

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 5 лет назад

you are stupid sorry

@Alkim_gercek 7 месяцев назад

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

@nocturnalvisionmusic 3 года назад

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

@matthewgarrett1996 7 лет назад

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 4 года назад

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

@FKX33 12 лет назад

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.

@nexisle7508 7 лет назад

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 :)

@Nandine2 15 лет назад

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

@conconhelp 12 лет назад

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

@gago776 11 лет назад

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

@carloscordova9293 6 лет назад

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

@noblessus 15 лет назад

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 3 года назад

11 years later your comment got a reply

@noblessus 3 года назад

@@ameershahul2968 hurray! lol

@ameershahul2968 3 года назад

@@noblessus 🤣I thought you wont reply

@singingsincebirthtb1418 2 года назад

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

@ameershahul2968 8 дней назад

you there bud we meet again

@Rboysblaster 11 лет назад

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.

@handlethatsavaildable 9 месяцев назад

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

@GreetingsItsEva 11 лет назад

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.

@EDUARDO12348 7 лет назад

The graphs of the arcsigns look interesting.

@denizemil7559 3 года назад

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

@asemnafiz 11 лет назад

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 RU-vid.

@qualquan 9 лет назад

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 9 лет назад

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 9 лет назад

qualquan It doesn't work like that

@classicalbhargav 7 лет назад

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

@Flipside2099 6 месяцев назад

Sin? Makes so much sense. Thanks bro

@bkboggy 9 лет назад

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 6 лет назад

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 6 лет назад

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.

@ashleyching5786 Год назад

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

@myaccc123 15 лет назад

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

@callitasisee 14 лет назад

@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 :)

@Handle12456 4 года назад

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

@roachey15 13 лет назад

@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.

@JustinGarfield1 3 года назад

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?

@WishingStarflakes 11 лет назад

this man saves lives

@frery5 8 лет назад

thanks

@OlofTheBald 13 лет назад

@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.

@BruceLeefromthegrave 12 лет назад

You are welcomed.

@mybloodyvacuum 11 месяцев назад

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

@soccerman1434 14 лет назад

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.

@star0dust8 5 лет назад

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

@droma51090 12 лет назад

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

@vuthao6290 Год назад

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

@VeritasEtAequitas 4 года назад

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?

@DinoRiott 14 лет назад

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

@florentinosanchez3969 9 месяцев назад

Best video ever. Thank you so much for making It

@wetim99 12 лет назад

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

@puzzlepeace19 13 лет назад

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

@puzzlepeace19 13 лет назад

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

@thenewguy461 13 лет назад

@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.

@itzyfan88 Год назад

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

@marxianus 6 месяцев назад

How do you know at 8:05 that this is 30-60-90 triangle? It doesn't seem to be obvious...

@rudylawson5552 6 лет назад

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

@xcstacy2 14 лет назад

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!

@viewlesspanda2429 Год назад

bless this man

@unsalad Год назад

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

@1piecemage 13 лет назад

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

@richanddarksbane1439 9 месяцев назад

really really good explaination

@Teymur69420 8 месяцев назад

I agree

@ClaudioBOsorio 4 года назад

Thanks a lot sal. Never stop!

@BigMotion1 26 дней назад

It's like arc functions are the logarithms of trig

@Rboysblaster 11 лет назад

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

@Ren-ITe 3 года назад

We really need to keep this man off the streets.

@NoirNeko333 5 лет назад

Love the way you say "two"

@valentinacalivano8436 11 лет назад

why do we only use the first and fourth quarts only ?

@themin91 12 лет назад

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

@hammurambi 12 лет назад

Excelent explaination. Thanks Sal.

@nickgrqlkimd21 8 лет назад

Thank you ! That was really helpful

@anniemarieevans08 14 лет назад

Love your stuff! What software are you using?

@FredrichNietzsche25 13 лет назад

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

@matassadaunykas4785 4 года назад

a very helpful video

@PBxTHExNIKExSBxOGx 13 лет назад

alg. II (adv) final tomorrow. THANKYOU!

@WolvesOfAtlantis 12 лет назад

I live for the day this guy learns grammar.

@wrxmomo1 11 лет назад

Yes - they are the same thing!

@mitch6145 10 лет назад

Isn't there 2 answers? 5pi/3 and 4pi/3? Since sin is negative in both the 3rd and 4th quadrants? I dunno if I sound stupid or something but please explain?

@j0shua1208 9 лет назад

That is true, however in order to make the function one-to-one, sin must fall between in either Q. I, or Q. IV. Which means it must be 5pi/3, however that doesnt fall in [-pi/2, pi/2] , which is why one must convert it to -pi/2.

@davidmetz9499 6 лет назад

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 4pi/3 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.

@PaProblem 7 месяцев назад

Thanks

@PacesetterAbbey 8 лет назад

Nice explanation! Why is Sin^-1 (π) undefined ? For example, why is this question undefined ? >>>>> sin(sin^-1(π))

@akshaysingh876 8 лет назад

+PacesetterAbbey Because arcsin can take values only from -1 to 1. That is, the domain is (-1,1). Since pi is not there in the domain, the function is undefined.

@Nobody-Nowhere-Nothing 7 лет назад

+Akshay Singh Wrong, arcsin can only take values from pi/2 or -pi/2 anything beyond or below that is undefined.

@droma51090 12 лет назад

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

@EaglesFastAndLow 12 лет назад

This is absolutely amazing.

@dltltr 12 лет назад

I like how I know the answers already.

@AmitKumar-ho3mr 6 лет назад

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

@SonjaPond 12 лет назад

Ermahgerd! Thank you, Khan Academy!!!

@AOTDagents 11 лет назад

I LOVE this guy omfg

@badriprasadmishra8715 6 лет назад

Find the minimum value of inverse of tan( cosx+ sinx)/( cosx- sinx)

@badriprasadmishra8715 6 лет назад

If x

@sarablack10 12 лет назад

Thank you very much!

@strtg3y3r 11 лет назад

This is very helpful

@encryptedpenguin3220 Год назад

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

@virtuoustex 8 лет назад

Thank You!

@lukoshke 14 лет назад

Thanks a lot man!

@BrianJFagan 11 лет назад

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)??