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eliminate arbitrary constant y= A cos ax +B sin ax

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Answer to a math question eliminate arbitrary constant y= A cos ax +B sin ax

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Fred
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La identidad es cos(a + b) = cos(a)cos(b) - sin(a)sin(b). Podemos reescribir y = A cos(ax) + B sin(ax) como y = R cos(ax - φ), donde R es la amplitud y φ es el cambio de fase. Aquí, R = sqrt(A^2 + B^2) y φ = atan(B/A). Entonces, la ecuación y = A cos(ax) + B sin(ax) se puede reescribir como y = sqrt(A^2 + B^2) cos(ax - atan(B/A)). Esta forma de ecuación elimina las constantes arbitrarias A y B. Esta transformación supone que A ≠ 0. Si A = 0, el cambio de fase φ sería π/2 o -π/2 dependiendo del signo de B.

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