What are the necessary trig functions for finding the rotation formula?

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The discussion centers on deriving a rotation formula for a function of a 3D vector, specifically involving the superposition of four distinct functions represented as f1, f2, f3, and f4. The user seeks a mathematical expression that incorporates trigonometric functions to achieve this superposition. The conversation highlights the necessity of understanding angles, particularly Euler angles (α, β, γ), to facilitate the rotations from one vector configuration to another.

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  • Basic concepts of vector summation and superposition
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Ben Wilson
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I have a function of a 3 vector, i.e. f(+x,+y,+z) [ or for conveniance f=+++]

this function is repeated 4 times where:

f1 = + + +
f2 = + - +
f3 = - - +
f4 = - + +

I need a formula where i have a different vector for each function in a summation, to obtain the superposition of all 4 functions.

I'm having a nightmare trying to find a rotation formulae, can anyone help?

i'm guessing there will be some trig functions involved somewhere.
 
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Ben Wilson said:
I need a formula where i have a different vector for each function in a summation, to obtain the superposition of all 4 functions.
Can you state that formula?

Ben Wilson said:
I'm having a nightmare trying to find a rotation formulae, can anyone help?
What do you mean by "rotation formulae"?

Ben Wilson said:
i'm guessing there will be some trig functions involved somewhere.
Do you need to figure out the angles (like Euler angles) necessary for those rotations? Like knowing that you go from +x,+y,+z to -x,+y,+z by a certain combination of α, β, and γ for a given +x,+y,+z?
 

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