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(1) Why sin(30) = 1/2 ?
(2) i ^ 2 = -1 = rotation by 180°
(3) Transpose [A] = Rotation by 180.
(4) Diagonal of a matrix = Its axis of rotation.
(5) Why A x B = ABsin( )??
(6) Why Log(A x B) = Log(A) + Log(B) ???
(7) What is the purpose of curl and divergence??
(8) Purpose of differential equations.
For (6$)
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Solve the Indefinite Integral with Complex variable.
Calculus--Indefinite Integrals (05-25, total: 288) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw
https://youtu.be/8tLMnAdxb4U

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1] How sin( ) is a measure of how much perpendicular two objects/forces are.

2] How cos( ) is a measure of how much parallel two objects/forces are.

3] How in complex numbers
i = rotation by 90 degrees
i^2= rotation by 180 degrees
i^3= rotation by 270 degrees.
i^4 = rotation by 360 degrees.

4] Transpose of a matrix = Rotation by 180 degrees around the diagonal.

5] e^i(angle) = rotation by that angle.

6] sin(30) = 1/2
because at 30 degree the effect of a force reduces to half over the other force/object (as against when the two forces/object are against at 90 degrees w.r.t each other)

7) A X B = |A| |B| sin(angle between A and B)
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1] Sin( ) is a measure of how much perpendicular two objects/forces are.
2] Log(effect) = cause,....10^cause = effect.
3] Transpose of a Matrix = Rotation by 180 degrees.
4] i = rotation by 90 degrees,....i^2 = rotation by 180 degrees, i^3 =rotation by 270 degrees.
5] e^(i.any angle) = rotation anticlockwise by that angle.: e^(-i.any angle) =rotation clockwise by that angle.
6] Cos( ) is a measure of how much aligned two forces are.
7] Diagonal of a matrix is its axis of rotation.

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