Sine and cosine from rotating vector

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www.khanacademy.org/science/e...
One way to generate sine and cosine is to track the motion of a rotating vector.

[@intrepidolivia482]

No matter how many times I learn the concepts of sine and cosine, I can never quite seem to remember what they mean in a geometric sense. This animation is incredibly helpful as a refresher.

[@ull893]

4 minutes of animation better explains than 2 hours of lecture 😊💖thank you

[@bob-ny6kn]

Pay attention during lecture. The world has learned trig without video, but you need video? I can guarantee you were doing everything BUT paying attention.

[@yashasvi_karsh]

@@bob-ny6knsuch an irony.

[@azi9_ity]

@@bob-ny6kn guy named bob:

[@ju5e3]

​​@@bob-ny6kn you are one salty mfer. Are you a teacher yourself? You were spamming these comments for some reason. If so you should know that gaslighting kids won't make you better at your job.

[@ozanh]

The video is just the way to reach many people, I would literally explain co-sin to a kid with a toy wheel and a nail. So shame on math teachers, most of them not talking about the logic but only formulas.

[@am_i_blue]

Our teacher made this so boring that i couldn't even focus on what he was saying plus he took a whole period. And here in 4 mins,this thing is printed in my mind. It's time to change the way of teaching in schools

[@bob-ny6kn]

Maybe if you paid attention it wouldn't be boring. The unit circle is taught the same everywhere, sin, cos, tan, csc, sec, cot. pi/6 through 2pi radians. The problem is all you.

[@am_i_blue]

@@bob-ny6kn oh so you are the one who had a cctv camera installed in our classroom and could see everything i could

[@spacejunky4380]

The projection a co-sin on the x axis is the best way I seen to understand how it works! Also, when you showed the projection of the sin wave changing over time helps my grasp a little more what rotating vector over time means for a sin wave.

[@digitechconsult5186]

I love this very educating and inspiringly simplified

[@gauravbagra9177]

VERY HELPFUL!! THANK U!!

[@mohfa1806]

hello , and thanks for your great educational videos..i have a question pls , i cant imagine how the green vector is rotating at constant velocity while the yellow dot is moving in variable velocity although it is the projection of something moving at constant velocity ? , is there a proof for that ?...thank you in advance

[@saurabhmishra2132]

very helpful and clear...

[@scarlettjohansson3142]

What software do you use for handwriting input in this video?

[@volcanowb]

What program are you using to animate?

[@orenkrimchansky]

thats powerfull bro!

[@igorg4129]

Thanks so much. Real great

[@dalenassar9152]

At THETA=0, I see that COS is "1" and DECREASING, but HERE, shouldn't SIN be "0" and RISING--instead of FALLING??

[@Johannes00]

Can you find the speed of something which rotates around a target by measuring the time it takes for the projection of the rotating object to go from top to bottom on the y axis with speed = distance / time?

[@Gorgutek1]

Yes, but as the "distance" you have to use half of the circuit, not the straight line between top and bottom.

[@steadyeddy6526]

Yes, very beautiful and fundamental

[@laomark9583]

Thank-you !

[@curtpiazza1688]

Cool STUFF! 🎉

[@gohancolores]

It's beautiful, you can See this pattern while someone is playing with a rope

[@doce7606]

Great. Q: the x and y axes are orthogonal; are the vectors of the two functions at their crossing (intersection) points either orthogonal (3.16) or parallel (3.10); if not what is the relation?

[@justasydefix6251]

Hey! Do you know where can I find 3-phase analysis? Thanks in advance.

[@diamondbackdtb]

how do you program the unit circle with a vector rotating

[@bob-ny6kn]

Pythagorean theorem for a triangle can be used to find the end of the radius so you can draw a circle. It is where the sin side and the cos sides meet: for (float i=0; i

[@eng.algareebsaudi1648]

The best 👌

[@sir_john_hammond]

Is that really a cosine though? I thought a cosine is in the same direction as the sine but 90 degrees out of phase.

[@yassermahamad565]

they are indeed out of phase ..but he is just drawing them in the same time but you still can see that shift if you pause the video for a moment .

[@dougwarner59]

I thought a cosine wave had to be a function and what he is showing is NOT a function. Cosine functions have a domain of (+- infinity) and a range of (+- 1) (which this does not) also a functions has to pass the vertical line test which it does not. Maybe he's doing it this way to make it more unique looking since I have never seen the cos and sin shown on different axis before. I have seen them shown doing this same circular rotation but both were on x axis.

[@SubVengeance]

They are indeed out of phase. If you rotate the cosine horizontally you can see the 90 degree shift.

[@bob-ny6kn]

He was showing sin(x-pi/2). Functions can have only one result, or they are complex/imaginary.

[@obaidaja8959]

Sir I'm a mathematics teacher and I need the name of program that you did this graph

[@kamalbhaizan]

yes that would be helpful!

[@mannb1023]

Ah yes, indeed

[@NN-zs7vd]

learn a programming language and you can do it yourself

[@bob-ny6kn]

How can you (all) be teachers an not know where to find simple resources? Liars.

[@hekk_tech5975]

sine-cosine hypnosis

[@-Saicharan-ro2ks]

superb sir thanks a lot

[@stevecallachor1]

I understood what sine and cosine meant until I watched this demonstration…………….K I S S the principle of learning!!!! Stavros

[@Farzriyaz]

I can actually do that on desmos 0:50

[@999luckyjohan]

wooo nice

[@matthewbrennan3127]

FIRST I LOVE YOU SAL

[@96oscarC]

its not sal in the video

[@muhammadm4582]

Why thetime axis unit is pi?

[@bob-ny6kn]

Pi radian = 180 degrees

[@TroyaE117]

My friend, marvelous animations but w is not the frequency. w is the angular velocity. The frequency is w/(2*pi).

[@altuber99_athlete]

It's the _angular_ frequency.

[@monoman4083]

top dollar info pic...

[@thesmiler119]

Green line- hypotenuse

[@bob-ny6kn]

Radius

[@rob7476]

lmfao. so many years of calculus and just figured out how a sine/cosine differs /how they're created. Oh, youtube

[@bob-ny6kn]

Were you really that absent a student? Teachers repeat this stuff day after day. You needed to listen.

[@rob7476]

@@bob-ny6kn they dont explain it well, practically. My doctorate must mean I'm dumb, tho

[@jabobthegod]

I came here to only see the wave lol

[@Marcara081]

And then two madmen use this to map politics.

[@dalenassar9152]

...was I focused on the "PAST"?

[@Adityau-pn7bj]

Rajwant sir ke class me kon kon ise dekha hai

[@HanzCastroyearsago]

Hm

[@habibsafi9122]

ASSALAMO ALAIKUM KHAN G SANGE YAR MUNG THA DA BEJLAY FILTAR P KAR DE CHE DA BA SANGA SAZZ KO

[@jameswilson2110]

Gundam anyone?

[@user-zl4zf7wt7s]

これ、マイナス方向に動いているみたいにみえるから 三角関数の学習者としては分かりにくい

[@smoothestones1]

What's your vector, Victor? *waves* Do you need a sine to get pregnant? It's all math.