AngouriMath
SolveByExpandingATrigonometricPhaseBesideAnExponential(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A sine or cosine of a linear form with a phase, beside an exponential, expanded by the
angle-sum identity so that both are of the same bare multiple of the variable:
cos(f x + p) is cos(p) cos(f x) - sin(p) sin(f x) . The closed rule for a
polynomial times an exponential times a trigonometric reads one frequency and no
phase -- an exponential's own offset is a constant factor, a trigonometric's is not --
and a phase is what every row of Rubi's 4.3.10 and 4.4.10 carries once
A + i A tan(pe + f x) is written as an exponential over a cosine.
angle-sum identity so that both are of the same bare multiple of the variable:
polynomial times an exponential times a trigonometric reads one frequency and no
phase -- an exponential's own offset is a constant factor, a trigonometric's is not --
and a phase is what every row of Rubi's 4.3.10 and 4.4.10 carries once
Remarks
Only beside an exponential of the variable, which is the shape that rule answers: the
expansion doubles the terms of every sine and cosine it touches, and the sum split
would then answer `sin(a + b x)` as two integrals where one closed rule answers it as
one. Once: the expanded form has no phase left.
https://github.com/asc-community/AngouriMath/issues/718
expansion doubles the terms of every sine and cosine it touches, and the sum split
would then answer `sin(a + b x)` as two integrals where one closed rule answers it as
one. Once: the expanded form has no phase left.
https://github.com/asc-community/AngouriMath/issues/718
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