Law of sines | Trig identities and examples | Trigonometry

Law of sines | Trig identities and examples | Trigonometry | Khan Academy

Рет қаралды 1,106,391

10 жыл бұрын

Practice this lesson yourself on KhanAcademy.org right now:
www.khanacademy.org/math/trig...
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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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Пікірлер: 248

@n8125 4 жыл бұрын

the raw power in how he casually notes that in a later video he will prOVE the law of sines is exhilarating

@luxmin6115 4 жыл бұрын

Chaotic neutral

@memyselfandtau4712 2 жыл бұрын

Agreed

@stoptrynakillme1952 5 жыл бұрын

who else has a test tomorrow?

@nathanciocca7870 5 жыл бұрын

More like 30 minutes...

@stoptrynakillme1952 5 жыл бұрын

Nathan Ciocca good luck lol

@codvx 5 жыл бұрын

2 hrs...

@analyssahicks8919 5 жыл бұрын

zyrs aye did u pass?

@analyssahicks8919 5 жыл бұрын

zyrs cause I got a test tmmr and need some ‘assistance’ if u get my jist

@empirehypnosis 6 жыл бұрын

Spaced out during discussion. This is actually surprisingly simple.

@j.p.rogers6731 4 жыл бұрын

ha me every day

@sampitman3630 4 жыл бұрын

Very cool user name

@jeffreyschumacher1282 6 жыл бұрын

Thank you so much man I had a test for trigonometry and this was the only thing I dind't get at first. I got 90% on it

@shrutinagory7449 3 жыл бұрын

good job 👏

@CopingLoser 2 жыл бұрын

nice

@sprtzedits-ei7el 4 күн бұрын

trash

@cherrycheese2746 2 жыл бұрын

This channel is the only reason im passing math

@jjmanson7622 4 жыл бұрын

Made it MUCH more complicated than it really is with NOT just cross multiplying and having more accurate numbers than if you do the approximate from the beginning. But it's your prerogative on which you method you like best.

@HamzaAbdulFattah 3 жыл бұрын

RIP everyone with 2 sides and an angle watching till the end

@nicolasalvarez2052 3 жыл бұрын

Wait what?

@2centzincorporated658 3 жыл бұрын

cosine law baby

@kristv6496 2 жыл бұрын

what why

@bookman9897 2 жыл бұрын

@@kristv6496 that's found by cosine law

@narekkazarian4943 10 жыл бұрын

Great memory refresh for Law of Sines. Thank you Sal

@thisisit595 4 жыл бұрын

Narek Kazarian how are you now?

@cullenwilliams1695 3 жыл бұрын

My teachers do a horrible job of explaining this, this is so much simpler then I thought

@ebruhhk 7 жыл бұрын

Im failing math. ☹️️ this shit is top hard

@arianareyes1708 7 жыл бұрын

Ibrahim Karra-Aly same.

@neainez6376 4 жыл бұрын

Anyone else foing this in geometry

@matthewhickling1350 3 жыл бұрын

imagine getting through highschool math without khan academy

@GeoMathLab 2 жыл бұрын

Always a pleasure viewing videos from the veteran of online teaching. Working my way to get to your level, Mr. Khan. 💯😎

@AndreatheSupremeCommander 8 жыл бұрын

May God bless your soul. I needed so much help. Thank you so much :)

@davidmateus7871 7 жыл бұрын

chicken massala

@MrNoSIeep 4 жыл бұрын

David Mateus I have no idea how you managed to get 22 likes by simply writing chicken massala, but you did, on a mathematics video no less. This has encouraged me to sub to you.

@Mochi-pk2vc 3 жыл бұрын

@@MrNoSIeep LMAOO

@mohammedhamdan1965 2 жыл бұрын

@@MrNoSIeep 50 likes lol

@bn4891 7 жыл бұрын

Best video, thank you!!

@griffinleggieri2885 6 жыл бұрын

Why don't you just cross multiply?

@huntforerror 5 жыл бұрын

yeah had that same inquiry...

@Angelica-ec7tv 5 жыл бұрын

My teacher taught us to just cross multiply and divide if needed

@kirstenmilliron3715 4 жыл бұрын

Yes, just cross multiply. Tons easier.

@chasemurray7633 4 жыл бұрын

Fax

@LB-gc2rv 3 жыл бұрын

My teacher taught me different, he suggested that you just try to solve for the variable like a normal algebra equation, so we would have b over sin of 45 = 2 over the sin of 30, the he said to solve for b you could just multiply both sides by sin of 45, leaving you with b = 2*sin45 over sin of 30, and then you would type it into the calculator exactly how it is and get the answer for b, I know it seems like a lot of steps but it's not, it's just plain old algebra 1, I feel more confident using this method then cross multiplying, I'm really bad at explaining things about math concepts but hopefully you understood that. Also, this method feels faster to do in my opinion, it may be different for others, whatever way you feel comfortable solving it is good.

@onedgivesmelife5741 8 жыл бұрын

Topped the class bc of this THANK YOUUU

@harishgoswami7275 4 жыл бұрын

Oh man! Wonderful... As usual..

@michaeltimmons8135 7 жыл бұрын

i honestly hate this stuff

@Nick-kb2jc 6 жыл бұрын

So you hate life and the fundamental nature of reality?

@yuayua2737 5 жыл бұрын

Why?

@notagoodpilot8161 4 жыл бұрын

Nick yes

@ziadyasser2854 4 жыл бұрын

dude the fact of nature connection between nature and logic and maths is just exciting

@saumyapatel7750 3 жыл бұрын

Dude be happy I am in 7th grade and I have to watch this what I don’t even know

@diya9707 6 жыл бұрын

Thanks! This video made my day ;)

@KarlSnyder-jh9ic 2 ай бұрын

I like the lecturer's style. I know this prob is easy like pie, but I gotta start somewhere. Excelsior!

@AngelaaJoyy 6 жыл бұрын

Thank you so so much this is great

@2oqh Жыл бұрын

thank you very much this was very concise & overall helpful

@6figures6problems 8 ай бұрын

Thanks this helped so much

@omegamagna 2 жыл бұрын

Why does every other video I look up not make it this simple? Khan Academy coming in clutch again

@lainiesilleto8965 3 жыл бұрын

greatest six minutes i've spent all week

@adityaadit2004 5 жыл бұрын

I've just learned this now

@dae1925 3 жыл бұрын

THANK YOU SO MUCH

@tonysherif9658 5 жыл бұрын

thats so helpful

@akacracka4629 6 жыл бұрын

he makes simple steps so complex

@csfhusker5874 3 жыл бұрын

this service deserves WAY more money then 70 thousand dollars

@tamtamyaystar 10 жыл бұрын

Thanks a lot you explained it really well

@louieryannadela6262 4 жыл бұрын

In the side b you can just put b=4sin 45°=2.828 and round off it and the answer is 2.83

@krishnasalunke3254 3 жыл бұрын

Love u!

@ohhesnumb4409 Жыл бұрын

thanks

@mathematiccrap867 4 жыл бұрын

Thanks you saved me Khan. I got be on my meth test

@samuelfeaster8265 5 жыл бұрын

5:37 “law of cosines”

@HunterHouse43 3 жыл бұрын

OH NO!

@tarfaibrahim912 9 жыл бұрын

1/4 or 1?

@tasneemsaad5270 3 жыл бұрын

Life Saver

@CaitlinIsBoring 5 жыл бұрын

I love your handwriting

@iamy4239 5 жыл бұрын

I text book says the equation is a/sinA=b/sinB=c/sinC

@codypendency9482 6 жыл бұрын

I don't understand why we have to learn this to graduate none of it has real life applications even as an engineer how often are you gonna need to figure out what the angle of a triangle is you'll just measure it out lol great video tho

@bando456 7 жыл бұрын

lmao 5:39 he said law of cosines good video though, helped me out.

@nickbastanfar6166 6 жыл бұрын

it confused me too lmao

@adamskead8859 5 жыл бұрын

Oh I see your using one side to solve the other, in homework for math I assumed I'd have to solve one side before I can solve the one I wanted to solve first

@charlesseadschlag7193 2 жыл бұрын

this guy is the life blood of procrastinators the night before a test.

@SY-tz3um 4 жыл бұрын

100x better than my lecturers

@amarat. 2 жыл бұрын

got 94 on the test the next morning lol thanks g

@whatsupbudbud 6 жыл бұрын

Would be nice if you'd explain the last part after multiplying the whole equation by "square root of 2 divided by 2". We ended up with b=4 times square root of 2 divided by 2. I got the correct end result when I: 1) Got the square root of 2. 2) Divided that result by 2. 3) And multiplied that by 4. But the author of the video just divided 4 by 2. Why?

@wilmot_ 5 жыл бұрын

Bless

@atilamotila8907 7 жыл бұрын

When doing the equation why didnt u just use times then divide and get missing value its legit much easier

@geminiwonder867 5 жыл бұрын

I can't believe that there is almost 1million views of Law of Sines

@yerrrrrrrr4567 3 жыл бұрын

online school make me wanna stop breathing. this helps tho

@lilreddy6669 6 жыл бұрын

Can you cross multiple to get sin30(A)=Sin105(2) But then what would you do from there

@ThinkLuckyThink Ай бұрын

Getting ready for finals………………………*sigh*

@grimreaper1655 7 жыл бұрын

can someone tell me when you assume two solutions?

@a1sauce44 7 жыл бұрын

Grim Reaper it's 2016, u can't assume solutions

@multicoloredrainbow 4 жыл бұрын

@@a1sauce44 It's 2019, you still judge people on their knowledge (or lack thereof)? Or have you grown up and quit being such a judgmental shoelace?

@darscoll1073 7 жыл бұрын

This is the hardest

@bella-pg6mn 6 жыл бұрын

r u serious what abt simultaneous equations with quadratics

@myspacebarbrokenevermindif9892 6 жыл бұрын

Dars Coll nah, it gets much... much much much MUCH harder than this

@muhammadnafis8412 8 жыл бұрын

how could people dislike khan academy

@Tolderian 8 жыл бұрын

People who are bad at teaching. They jealous.

@dolllover1987 6 жыл бұрын

He can be confusing sometimes.

@unsolicitedd 5 жыл бұрын

Cause they hate math

@jessicagonzalez8601 4 жыл бұрын

Someone do my homework and I’ll pay 😭

@aringupta4883 2 жыл бұрын

Thank you so much! Extremely helpful - although you said law of cosines at 5:39

@santoryu8940 7 жыл бұрын

when equating sin(30)/2 and sin(105)/a, i noticed that you evaluated sin(30) and left sin(105) alone. My question is, what if i also evaluated sin(105) and proceed to solving for a, do i still get the same value for a?

@neainez6376 4 жыл бұрын

This comment scares me

@obesehoraffe1070 6 жыл бұрын

wouldn't you have to multiply the 2 square root of 2 by 4 at the end though? what happens to that 4?

@danielreyes4997 6 жыл бұрын

Same question here :(

@danielreyes4997 6 жыл бұрын

Figured it out. if you multiply sin45 4 times it would give you sin135 which would still land in square root of 2 over 2. also, you can use the calculator and multiply sin of 45 by 4 and would give you the same answer he got.

@tatiyannasparks8934 4 жыл бұрын

Yeahh imma fail the quiz but imma go to tutoring 🙁

@lunaeclipse5768 Жыл бұрын

i think sal should remastered his pre-algebra and pre-calculus course that doesnt have 720p quality like this not hiring other person but if the person is related to him then okay, thats fine

@stoneymaloney844 3 жыл бұрын

How is Sine calculated? Like when you plug in the sine of an angle on a calculator how is that calculated?

@aairavkalra1711 2 жыл бұрын

we don't question it

@azura4582 3 жыл бұрын

is there a video on 2 sides 1 angle? ik its the same buututututt i need exampleee

@pablo8524 6 жыл бұрын

how did you get 1 over 4?

@Y0ug0glenc0co 8 жыл бұрын

ilysm

@austinmiller3957 3 жыл бұрын

where did the sq root of 2 over 2 come from?

@Name-em6re 2 жыл бұрын

That man has mad skills if he is writing with a mouse

@mariobros4146 3 жыл бұрын

10% of the video: actually explaining what to do 90% of the video: a bunch of random stuff we don't need to know

@VanillaSkyy18 3 жыл бұрын

Exactly, this guy can barely talk 😂

@harshithgowni1528 4 жыл бұрын

If they didn't teach this to me in school....... *how do they expect me to do this?*

@IsaaaValorant 2 жыл бұрын

yeah thanks for showing it with round numbers -_-

@smac9273 7 жыл бұрын

Can you figure out everything if you only have two sides with no angles?

@user-gz1vd2ge5f 6 жыл бұрын

Well, it's very easy to understand. Korean high school students learn this in their sophomore.

@ampharos3106 6 жыл бұрын

huh I’m a sophomore in America and I’m learning this

@emilyb6682 5 жыл бұрын

yeah trig is literally highschool math whats your point

@reptilprinceoflizardpeople5797 5 жыл бұрын

Kim Jong Un gonna nuke anyone soon?

@livingtribunal8456 7 жыл бұрын

how did it became 1/4?

@julietten5614 6 жыл бұрын

good question)))

@gangsterlean7300 5 жыл бұрын

Exactly like tf

@mattxgaming4053 4 жыл бұрын

Living Tribunal *from the future* .5/2 is the same thing as 1/4

@cottoncandy295 7 жыл бұрын

I don't get the reciprocal part... Is there another way?

@tamircohen1512 7 жыл бұрын

Simply put, if you take the reciprocal of two fractions which are equal to each other, the fractions remain equal. For example, say x/y = a/b. This would mean that y/x = b/a. Another example with actual numbers is 4/2 = 2/1. This is equal to 2. If we take the reciprocal of these fractions, we get 2/4 = 1/2 and as we know, 2/4 is 0.5 and 1/2 is 0.5 so the fractions do in fact remain equal.

@Aninjacow100 7 жыл бұрын

Very clear, concise explanation, but sadly 6 months late :)

@noobynoob6856 5 ай бұрын

This is cool but I don’t get why I get a different answer for the hypotenuse when I take the cosine of 45 which is around 0.7 and get 0.7/1=2/x and do 2/0.7 which is around 2.85 and multiply that by 1 getting x=2.85 did I do something wrong

@irelyn211 3 жыл бұрын

how do you do this if you have sin40/5 = sin b/f = sin c/7

@akaBaye 6 жыл бұрын

just wondering what grade you guys are learning this? how old are you ? just curious as iam behind and learning this right now. I’m 16 years old. is that a normal age to learn this ?

@dolllover1987 6 жыл бұрын

I'm 13, but I'm preparing for this huge high school test.

@charminglife6150 5 жыл бұрын

I learned it at 16, didn’t use it for 31 years, now am relearning so I can become an engineer! You can learn it at any age once you’ve learned enough geometry to handle it.

@rushilpatel7418 3 жыл бұрын

Please please nominate this guy for knighting and for every other highest citizen honour in the mutiverse.

@katystacy1279 4 жыл бұрын

Everyone in the comment is like oh yeah I get it. I'm over here stressing because midterms are tomorrow and this is basically all my test is on but I still don't get it.

@KINGOFGUITAR2101 7 жыл бұрын

If he had kept the one half over 2 it would be a different answer no?

@MrSmith-vz3in 7 жыл бұрын

He sounds like a youtuber ImMarksmen

@Youssefelbaz7 7 жыл бұрын

Lol...

@bjjeffries8172 5 жыл бұрын

Is there any reason why you didn’t just “cross multiply” once you set your ratios equal to each other? I can follow your method but my students get lost every time. Just wondering if I’m missing the reason behind that approach.

@Angelica-ec7tv 5 жыл бұрын

BJ Jeffries no in my class we just cross multiply

@AniematedSteph 5 жыл бұрын

The flaw is it teaches me with 30 degrees. That is easy because sin30 is known to be 0.5, and this doesn't teach us to do things that are, not 30, 45, 60, etc? (I feel like such a nerd writing this)

@EduardoKicks 10 жыл бұрын

can u figure everything about the triangle if u have only sides

@TofuFiesta 9 жыл бұрын

It kind of depends, you can use the law of cosines to figure it out, but after thorough testing I've found that the law of sines doesn't work in combination with the law of cosines, which is weird.

@elliottwood5423 5 жыл бұрын

he mentions proving the law of sines, where is that?

@patriciaflores2514 4 жыл бұрын

how do u know when the sin is on top or bottom?

@shawarmath9144 4 жыл бұрын

I suggest to put the missing info on top You can watch my video on it on "shawarmath"

@akashshinde4867 6 жыл бұрын

Make the diagrams more accurate and clear to visible, also have to work on font size.

@rubikscubing5634 5 жыл бұрын

Did anyone notice the mistake he said at 5:38 he said law of cosines

@MineCrafterCity 8 ай бұрын

I don't get it.

@jaidevramcharan4626 5 жыл бұрын

I'm here because I have my math exam tomorrow. 😭

@vitgrab6056 4 жыл бұрын

closer to the end of the video, don't you have to multiply the 2/-2 by 4?

@benw4361 5 жыл бұрын

Anyone know how he got the TI calculator onto his desktop?

@yotubeaccoutsuperawesome 5 жыл бұрын

Emulator. Just search TI calculator emulator. Should be called something like wabbitemu. You can get the same thing for Android as well. Just search the playstore.