ganeshie8 one year ago show that $$\sin(x)+\sin(x-120^{\circ})+\sin(x-240^{\circ})=0$$

1. ganeshie8

my roomate and i are arguing about electric motors and im looking for some geometric explanation for this..

2. Empty

what's true for x=0 is always true no matter how you rotate it

3. Empty

$e^{i x}(e^{i 2 \pi / 3} +e^{i 2 \pi 2/ 3} +e^{i 2 \pi 3/ 3}) =0$ the real part of that

4. Empty

imaginary part I mean, whatever, both are zero haha

5. Michele_Laino

it is a three phase system

6. rhr12

x + 120 = t sin(t - 120) + sin(t) + sin(t + 120) = 0 sin(t)cos(120) - sin(120)cos(t) + sin(t) + sin(t)cos(120) + sin(120)cos(t) = 0 2 * cos(120) * sin(t) + sin(t) = 0 sin(t) * (2 * cos(120) + 1) = 0 sin(t) * (2 * (-1/2) + 1) = 0 sin(t) * (-1 + 1) = 0 sin(t) * 0 = 0 So, sin(t) can equal pretty much anything t = x + 120 sin(x + 120) can be anything x + 120 can be anything x can be anything There are no wrong solutions for this one.

7. rhr12

That's all i got.

8. ganeshie8

Yes he is saying delta/star and some bs which i have no idea about... but it makes sense to think in terms of roots of unity as Empty wa suggesting.. (if im interepreting correctly..)

9. Michele_Laino

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10. Empty

x and y components of vectors are linearly independent in 2D. So in order for vectors to be in equilibrium in 2D their components must be in equilibrium too. That's what I'm saying

11. Empty

complex numbers are just a cute representation of 2d vectors I am so used to just thinking with them I forget other people aren't

12. ganeshie8

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13. anonymous

Confused

14. ganeshie8

welcome to the club @ruhan11

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