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

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

[3] 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 degree.

Transpose of (Transpose of) a matrix = Rotation by 360 degrees.

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

[6] sin(30) = 1/2 because at 30 deg the influence of a force/object reduces to half.

For example the shadow of a stick reduces to 1/2 at 30 deg.

[7] A x B = |A| |B|sin(angle btwn A & B).

total combined impact in cross product depends upon.. . . . .

how strong A is

how strong B is.

How perpendicular A and B are w.r.t each other.

e.g A ball hitting a wall will produce max impact at 90 deg.

Pdf book link

https://gumroad.com/l/visualizingmaths-e-bookBlog link

https://visualizingmathsandphysics.blogspot.in