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### Course: Electrical engineering > Unit 2

Lesson 5: AC circuit analysis- AC analysis intro 1
- AC analysis intro 2
- Trigonometry review
- Sine and cosine come from circles
- Sine of time
- Sine and cosine from rotating vector
- Lead Lag
- Complex numbers
- Multiplying by j is rotation
- Complex rotation
- Euler's formula
- Complex exponential magnitude
- Complex exponentials spin
- Euler's sine wave
- Euler's cosine wave
- Negative frequency
- AC analysis superposition
- Impedance
- Impedance vs frequency
- ELI the ICE man
- Impedance of simple networks
- KVL in the frequency domain

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# Euler's cosine wave

A cosine wave emerges from Euler's Formula. Music, no narration. Animated with d3.js. Created by Willy McAllister.

## Want to join the conversation?

- can you do a vid of both sine and cosine at the same time like this with music(7 votes)
- One of the best possible ways it can be explained. Thanks...(2 votes)
- Thanks.

Here's sine and cosine together: https://spinningnumbers.org/a/eulers-sine-cosine.html(4 votes)

- Why am I feeling that the adding is simply adding rather than vector adding, because if it is vector adding there will be squaring and rooting of the numbers.(1 vote)
- Notice there is a diamond shape rotating around. That is how you do a vector add.(3 votes)

- The background music is NirvanaVEVO by Chris Zabriskie.

It is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)

Source: http://chriszabriskie.com/uvp/, Artist: http://chriszabriskie.com/(2 votes) - set it at double the speed it sounds better,

ps. "Transcript" : (music playing)(2 votes) - is it possible to use sine, cosine, and tangent all in the same problem?(1 vote)
- I don't see why not. But I don't think it's necessary for AC circuit analysis.(1 vote)

## Video transcript

(music playing)