Sine and cosine from rotating vector

Keep going! Check out the next lesson and practice what you’re learning:

One way to generate sine and cosine is to track the motion of a rotating vector.

[intrepidolivia]

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.

[ull]

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

[spacejunky]

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.

[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

[digitechconsult]

I love this very educating and inspiringly simplified

[Johannes]

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?

[dalenassar]

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

[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.

[TroyaE]

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

[mohfa]

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

[Farzriyaz]

I can actually do that on desmos
0:50

[scarlettjohansson]

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

[TomHendricksMusea]

Wave or Helix, a look at the Electromagnetic Wave

The electromagnetic wave has both an electric field and a magnetic field. These are perpendicular to each other.

The illustrations online for the electromagnetic spectrum show a range of wavelengths from radio to gamma waves. But the illustrations show waves, never a helix. So which are they?

See my diagram. The electric wave is a vertical wave in red, and the magnetic wave is a horizontal wave in blue. They are perpendicular to each other.

Next see any of the numerous animated YouTube videos on sine waves and cosine waves. Mapping a helix or moving circle or spiral with a sine wave and a cosine wave, shows exactly the same thing as my drawing.

That seems to suggest that electromagnetic waves are not waves but helixes!!! This exactly fits a sine and cosine wave mapped as a helix, spiral, or moving circle.

This seems so obvious, yet I've never seen an electromagnetic wave represented as a helix or spiral. Has anyone else?

[volcanowb]

What program are you using to animate?

[obaidaja]

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

[stevecallachor]

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

Stavros

[doce]

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?

[AIWIZARDDT]

how do you program the unit circle with a vector rotating

[dalenassar]

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

[rob]

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