This is exactly how I think you are supposed to learn math - try to understand the exact reasonings behind things, so that you can derive them yourself on the spot.
Laurelindo This is a good way to learn simple math, but when you get into grade 12 (senior) year math and physics in highschool sometimes you get so many formulas and equations that it is much easier just to memorize them and what they are used for!
Yes, that's true - however, I think that one should always try to understand a formula as deeply as possible, as long as it isn't too time-consuming or complicated to derive. You could certainly get by with simply memorizing and using the formulas for calculating whatever an exam problem is asking for, but I think that formulas are always much more fun when I can sort of go through them in my head from beginning to end. I believe the first formula that I tried to derive myself was the Law Of Cosines, and when I succeeded I felt a great satisfaction, and I have been hooked since then, haha.
Irving Ceron Exactly. Formulas can be convenient if you want to quickly calculate something and you don't need to prove that you can derive those formulas, but it is a highly recommended practice to actually derive them from scratch every now and then. Personally I try to use as little formulas as possible - if you can derive something from the very basics then that's a good sign that you have a deep understanding for it.
In the beginning, there was the 4 mathematical functions: addition, subtraction, multiplication, and division. These 4 all lived in peace and harmony. But then, a great evil changed the mathematical world forever: X and Y. These letters attacked the peaceful world of the math functions, and the rest of the letter followed, leaving destruction and devastation in their wake. Only the Avatar, who mastered all 4 function could save us, but he disappeared. We most find a new Avatar to save our world!
As soon I saw the triangle being drawn by MS Paint-like lines, I knew this was an old video! 2007? That's near the beginning of Khan Academy. I was still a Freshman in high school when this video was made... wow.
I have been on a trigonometry marathon for the last three hours and my head hurts but the videos keep coming because of the playlist and essentially I can do nothing but watch.
Does it matter which two sides of the triangle you pick? The method shown can be duplicated by dropping an altitude from β and get sin(α)/A = sin(c)/C. But we already showed sin(α)/A = sin(β)/B, so by the transitive property of equality all three ratios are equivalent.
Thank you - I'm in need of a trig brush up and your concise explanation is just right for me. I always need to understand the derivation of formulas in order to remember them. Your simple explanation is very helpful.
At 00:49, the triangle has just one angle without name, and this is going to be gamma. So when you draw the perpendicular line to B you will have the same situation than in the video, rather instead of B and alpha you'll have gamma and A. Good luck! (this post is the following part from the former)
I was taught Some Old Hobo (Sine Opposite/Hypotenuse) Caught Another Hobo (Cosine Adjacent/Hypo) Tripping on Acid (Tan Opposite/ Adjacent) SohCahToa sounds like I'm speaking a different language
Nice job! The Law of Sines proof can take you to a higher trickynometric place. It's definitely NOT the height of absurdity although ALTITUDE is certainly involved. Thanks for a colorful and clear presentation. On a less goofy note, the relationship shown is an interesting one.
Just a question, i may not know much about trigonometry, but what's wrong with using two small right triangles to prove the law of sines? What was inconsistent? Also, how would you prove the law of sines? because i really do wanna learn about trigonometry and to see a different way of proving this would be really helpful.
More accurately, the opposite and adjacent sides are always relative to the angle you are solving for (or with). The hypotenuse is the longest side of a right triangle.
@TheNevikProject You're right, I've noticed it doesnt work in all triangles, its just hard finding those, or finding a relationship in those where it doesnt work.
He's dividing both sides by A and B so sin(alpha) and A are together on one side of the equation and sin(beta) and B are together on the other side. A and alpha are like partners, B and beta are like partners. They belong together.
I noticed a slight error at 5:58. (It also in the transcript.) You say "B over the sine of B," instead of "B over the sine of beta." I also noted that you used theta (the 8th letter) for the third angle, instead of gamma (the 3rd letter). I am a college math professor, I really like Khan Academy and am encouraging my 11-year-old son to use it to advance his mathematical knowledge.
@KhroniclesOfNothing I forgot that if there is no need to prove something that there is no reason to know something. Some people actually enjoy math and are interested in these things. Other people, learn better when they can understand why things are.
Actually, transitivity is not a law, is an axiom, so it CANNOT be proved, its a statement which needs no demonstration, it is simply true. Answering mephatboi, the process for getting sine gamma over C (or sine C/c) is the same, but in this case you are going to draw a perpendicular line to B that passes through beta.
This proof is somewhat disappointing because it only works on acute triangles. If he'd have drawn a triangle with an obtuse angle there would've been extra steps necessary, so the proof is not actually generalized. You can't draw an altitude resulting in a right triangle from the non-obtuse angles in that case.
@@chunkylover5367 sin(x) = (180 - x)?? i dont know if you made an error or not but for example: sin(90) = 1 which does NOT equal (180 - 90) = 90 1 does NOT equal 90, so therefore your claim has been refuted my good sire.
our math teacher taught us "Oscar Has A Hairy Old Ass" Opposite hypotenuse, adjacent hypotenuse, and opposite adjacent. I think I like SOH CAH TOA though
always skipping the hard part... it's not as clear as you think finding that last term. What makes you think that it would magically work if you don't show the proof?
This is exactly how I think you are supposed to learn math - try to understand the exact reasonings behind things, so that you can derive them yourself on the spot.
Laurelindo This is a good way to learn simple math, but when you get into grade 12 (senior) year math and physics in highschool sometimes you get so many formulas and equations that it is much easier just to memorize them and what they are used for!
Yes, that's true - however, I think that one should always try to understand a formula as deeply as possible, as long as it isn't too time-consuming or complicated to derive.
You could certainly get by with simply memorizing and using the formulas for calculating whatever an exam problem is asking for, but I think that formulas are always much more fun when I can sort of go through them in my head from beginning to end.
I believe the first formula that I tried to derive myself was the Law Of Cosines, and when I succeeded I felt a great satisfaction, and I have been hooked since then, haha.
Irving Ceron Exactly.
Formulas can be convenient if you want to quickly calculate something and you don't need to prove that you can derive those formulas, but it is a highly recommended practice to actually derive them from scratch every now and then.
Personally I try to use as little formulas as possible - if you can derive something from the very basics then that's a good sign that you have a deep understanding for it.
I actually hate math until i try to understand the reasons behind formulas , memorizing sucks, that's why many people think math is hard and boring
Exactly my thought,bro! The sad part is, you don't have enough time to derive the formulas and do the math in the exam hall though.
In the beginning, there was the 4 mathematical functions: addition, subtraction, multiplication, and division. These 4 all lived in peace and harmony. But then, a great evil changed the mathematical world forever: X and Y. These letters attacked the peaceful world of the math functions, and the rest of the letter followed, leaving destruction and devastation in their wake.
Only the Avatar, who mastered all 4 function could save us, but he disappeared.
We most find a new Avatar to save our world!
Great show
Great comment
"Hopefully that relationship will be the Law of Sines. Otherwise I would have to rename this video." LOL
🤣
As soon I saw the triangle being drawn by MS Paint-like lines, I knew this was an old video!
2007? That's near the beginning of Khan Academy. I was still a Freshman in high school when this video was made... wow.
haha this video is older than me
I wasn't even a year old. now I'm 17
this video is days younger than me
I have been triying to find this explanation everywere... thanks.
I have been on a trigonometry marathon for the last three hours and my head hurts but the videos keep coming because of the playlist and essentially I can do nothing but watch.
Thanks Sal, you never fail me
Thank you so much: you have just saved my math grade!
How's life 10 years later
@@alexmisra6690 Probably graduated from college and has a job
I was confused when i saw this law in physics......but now i understood it completely.......thank u
I still don't understand how to proof c over sinC equal to other
Does it matter which two sides of the triangle you pick? The method shown can be duplicated by dropping an altitude from β and get sin(α)/A = sin(c)/C. But we already showed sin(α)/A = sin(β)/B, so by the transitive property of equality all three ratios are equivalent.
Some Old Hippy Caught Another Hippy Trippin On Acid.
SOH CAH TOA!!
Excellent!
I memorised this, its the same:
sin(alpha)/sin(beta) = A/B
pewdiepie has 40 million subs
khan has 3 million
is it only me that thinks this is a little unfair?
everyone loves gay dudes
80 million now
@@prabinbhandari1180 90*
it's no 5Mil:109 mil or sumthin
Absolutely fascinating. Nothing more on the planet that I love than seeing mathematical proofs.
Thank you - I'm in need of a trig brush up and your concise explanation is just right for me. I always need to understand the derivation of formulas in order to remember them. Your simple explanation is very helpful.
At 00:49, the triangle has just one angle without name, and this is going to be gamma. So when you draw the perpendicular line to B you will have the same situation than in the video, rather instead of B and alpha you'll have gamma and A. Good luck! (this post is the following part from the former)
I was taught Some Old Hobo (Sine Opposite/Hypotenuse) Caught Another Hobo (Cosine Adjacent/Hypo) Tripping on Acid (Tan Opposite/ Adjacent) SohCahToa sounds like I'm speaking a different language
Dudeee you saved me, i prounounce things a bit differently and tend to mix up sohcahtoa. Im definitely using this🖤
Nice job! The Law of Sines proof can take you to a higher trickynometric place. It's definitely NOT the height of absurdity although ALTITUDE is certainly involved. Thanks for a colorful and clear presentation. On a less goofy note, the relationship shown is an interesting one.
Just a question, i may not know much about trigonometry, but what's wrong with using two small right triangles to prove the law of sines? What was inconsistent?
Also, how would you prove the law of sines? because i really do wanna learn about trigonometry and to see a different way of proving this would be really helpful.
Thanks a lot Sir. That's the best prove I found.
Quick and helpful! Thanks ☺️
he's bringing the equation down to the law of sines as seen, well everywhere you see the law of sines.
More accurately, the opposite and adjacent sides are always relative to the angle you are solving for (or with). The hypotenuse is the longest side of a right triangle.
i only wanted to see how u get the third part, sin C/c
but that's the part u skipped!
@TheNevikProject You're right, I've noticed it doesnt work in all triangles, its just hard finding those, or finding a relationship in those where it doesnt work.
He's dividing both sides by A and B so sin(alpha) and A are together on one side of the equation and sin(beta) and B are together on the other side. A and alpha are like partners, B and beta are like partners. They belong together.
thanks for teaching i have many troubles in math especially in trigo.
I noticed a slight error at 5:58. (It also in the transcript.) You say "B over the sine of B," instead of "B over the sine of beta."
I also noted that you used theta (the 8th letter) for the third angle, instead of gamma (the 3rd letter).
I am a college math professor, I really like Khan Academy and am encouraging my 11-year-old son to use it to advance his mathematical knowledge.
@KhroniclesOfNothing I forgot that if there is no need to prove something that there is no reason to know something. Some people actually enjoy math and are interested in these things. Other people, learn better when they can understand why things are.
16 years ago is crazy
just to clarify to proove c/sineC you draw a horizontal line across angle C and that would be h/a or or h/b?
Saw you on Colbert, congrats man.
4:02 good ole Transitive Property of Equality
Opposite and adjacent are always relative to theta. The 90 degree angle should always be opposite the hypotenuse (I believe)
Could you show how to use the law of sines to solve physics problems involving forces and vectors.
Can I figure out something in a non-right triangle that only gives me the area and the sum of the angles? I'm really wanting to know
Sum of angles is ALWAYS 180. As for area, you can use HERON'S FORMULA
oh men thanks for this video it helps me alote ^^
Thank you, I finally know how the equation came to be now :]
I need the proof of sine of beta over B equals to sine alpha over A equals sine theta over C "EQUALS TO 2R"? I saw that in some textbooks. thank you
hey can you show the other proof using area of triangle? thanks!
interesting, would be great to see sinus law in different dimensions
Wouldn't mind a remaster of this video its hard to read
ur a good man
Actually, transitivity is not a law, is an axiom, so it CANNOT be proved, its a statement which needs no demonstration, it is simply true. Answering mephatboi, the process for getting sine gamma over C (or sine C/c) is the same, but in this case you are going to draw a perpendicular line
to B that passes through beta.
Thanks sir...
Great Video
thank you
this video is high quality despite of 240p
This proof is somewhat disappointing because it only works on acute triangles. If he'd have drawn a triangle with an obtuse angle there would've been extra steps necessary, so the proof is not actually generalized. You can't draw an altitude resulting in a right triangle from the non-obtuse angles in that case.
Pollen Applebee quit making me feel bad
Not true. Sin (x) = (180 - x). Acute and obtuse triangles is the same case for sine. You’d be correct if it’s cosine.
@@chunkylover5367 sin(x) = (180 - x)?? i dont know if you made an error or not but for example:
sin(90) = 1 which does NOT equal (180 - 90) = 90
1 does NOT equal 90, so therefore your claim has been refuted my good sire.
@@rahulram4963 I think he ment to say sin(x) = sin(180-x)
@@yosephjeong3283 ah that makes more sense. ;p
you saved my life there :D
Tnx men
this is easy stuff but it would be much easier to explain if you used values
This video just put me 2 weeks ahead in my maths class xD
thx man,,,i was boutta fail my test lik real top.
our math teacher taught us "Oscar Has A Hairy Old Ass" Opposite hypotenuse, adjacent hypotenuse, and opposite adjacent. I think I like SOH CAH TOA though
How would that aid the proof?
This is sine rule, am i right?
oh mah god you can read the title? OwO
very nice
I wish you were my teacher
Why do you divide the equation; is there a reason?
To make each a side of the equation the ratio between it's angle and corresponding opposite.
is that.. MS paint??
oh...and your favorite word is aribitrary...i've noticed that
what about the proof of soh cah toa?
There's no proof. It's the definition of sinx ,cosx ,tanx respectively. In fact that's the mnemonic of the definition.
It's like basic definition , people who found trig defines the function as that kind of ratio
but soh cah toa is mnemonic
Nothing, using the law is just faster.
i remember Saint Oliver's Horse Came Ambeling Home To Oliver's Aunt.
What is this software
science uses greek letters to signify certain variables.
@PTL0
now THAT is True!!! ;)
Anyone watching in 2021 B)
Are you greek? You are using the greek alphabet. (alpha and beta)
ily
@daymare10110 u honestly made me lol irl
lmfao daymare XD
shoosh *pap*
This video explains nothing. So how do you do you solve the problem?
does not help my intuition....your a very intelligent showoff.
always skipping the hard part... it's not as clear as you think finding that last term. What makes you think that it would magically work if you don't show the proof?